Alexander ['Greek'] Thomson was born at Endrick Cottage, Balfron, on 9 April 1817, the seventeenth child of John Thomson and the ninth child of his second marriage to Elizabeth Cooper. John Thomson was the bookkeeper at Kirkman Finlay's cotton works there and had previously held a similar position at Carron Ironworks. Advancement with both firms was precluded by his strict Burgher beliefs which were shared by his wife: she had come to Balfron with her brother, the Rev John Cooper. The family was educated at home, partly by Cooper, but John Thomson died in 1824 and the family had to move from Balfron to the outskirts of Glasgow. Elizabeth died in 1828, leaving the family in the care of her son William, a brilliant classical scholar who was briefly professor of humanity at the University of Glasgow.

In 1834 William Thomson moved to London as a missionary, leaving his brothers and sisters at his house at Hangingshaw. In the same year Alexander became a clerk in a Glasgow lawyer's office. There his drawing skills attracted the attention of a client, Robert Foote, who had inherited the large plasterer's business of David Foote & Son in 1827 and had commenced practice as an architect in 1830. Foote's architectural practice was small but in association with the decorative plasterwork side of his business he had amassed a magnificent library and a large collection of classical casts from which Thomson learned much in the two years he was articled to him. In 1836 a spinal complaint obliged Foote to withdraw from architectural practice and Thomson completed his articles with John Baird, remaining with him first as assistant and later as chief draughtsman when much of his time was spent on the unbuilt college on Woodlands Hill. In the early 1840s Thomson's younger brother George, born at Balfron on 26 May 1819 was also articled to Baird, after recovering from a respiratory complaint which had been thought to be consumption.

On 21 September 1847 Alexander Thomson married Jane Nicholson, daughter of the London architect Michaelangelo Nicholson and granddaughter of the architect-writer Peter Nicholson. It was a double wedding, her sister Jessie marrying another John Baird ('Secundus') who, although an architect, had no family or professional connection with the Thomsons' employer. Born in Ayr in November 1816, Baird was some five months older than Thomson. He had been articled first to James Watt and then to John Herbertson before finding a place in the office of David and James Hamilton where he was, very unusually, named in the Directory entry. After David Hamilton died in 1843 and his firm was sequestrated in 1844, Hamilton's son-in-law James Smith continued his practice and John Baird commenced practice on his own account. After the financial problems of the Hamilton and Smith businesses were resolved Smith and Baird merged their practices as Smith & Baird. Their partnership does not seem to have been a happy one and was dissolved in 1848 when Baird invited his brother-in-law to join him, the new partnership being entitled Baird & Thomson.

Within two years the Baird & Thomson partnership was extremely successful with a large clientele for medium-sized villas and terraces of cottages in Pollokshields, Shawlands, Crossmyloof, Cathcart, Langbank, Bothwell and Cove and Kilcreggan. At Cove and Kilcreggan they enjoyed the support of the builder, railway contractor and ironfounder John McElroy who commissioned Craig Ailey in 1850 and built a considerable number of other marine villas either speculatively or for clients. These early villas were generally either Gothic, sometimes with Pugin-derived details, or Italian Romanesque but a few, most notably Glen Eden at Cove, had very original elements which, as Gavin Stamp has shown, have their origins in the publications of the architectural historian and theorist James Fergusson.

In 1854 Thomson began designing in a picturesque, asymmetrically-composed, pilastraded, neo-Greek idiom which derived from Schinkel at Rockbank, Helensburgh and the Mossman studio on Cathedral Street. These were followed by the Scottish Exhibition Rooms in Bath Street which he and some architect friends built to provide a Scottish counterpart to the period courts in the Crystal Palace at Sydenham. This decisive shift to the neo-Greek which would remain characteristic of him and by then had no counterpart either in Edinburgh or south of the Border was quickly followed by a change of partner. In 1856 the partnership of Baird & Thomson was amicably dissolved so that Thomson could form a separate practice with his brother George who may still have been in the office of John Baird Primus: the record is not absolutely clear. The new partnership quickly acquired influential contacts, notably the builder John McIntyre. Others were probably made through UP Church contacts.

In 1856-57 Thomson's architecture developed rapidly. The neo-Greek of Rockland achieved a much more sophisticated maturity in the Double Villa at Langside and his finest house, Holmwood at Cathcart. In the same years a more monumental but still asymmetrical Greek idiom was applied to church design at Caledonia Road UP, where both the lower façade and the tower were of Schinkelesque banded masonry. This banded treatment was extended into the adjoining tenement blocks for which he devised a repetitive bay design with pilastered first-floor aedicules and third-floor recesses containing anthemeon ornament. In the following year, 1857, this theme was further developed on a vast scale at Queens Park Terrace in which Thomson adopted his familiar device of linked Egyptian architraves set against a recessed wall plane and omitted the banded masonry. With subtle variations this formula was to remain a feature of his more upmarket tenements for the remainder of his career. The same motifs, now with a top-floor pilastrade, were to feature at Walmer Terrace and the first of his commercial blocks, 99-107 West Nile Street, both built in 1857.

In 1858 Alexander and George Thomson bought the Gordon Street UP Church in which they worshipped in order to build a showpiece warehouse with ground-floor shops - a fairly innovative concept at the time - in which the David Hamilton theme of interpenetrating pilastrades was developed into the same repetition of absolutely regular single-bay units, here much more complex in design, crowned by a deeply shadowed eaves gallery. It did indeed attract commissions for similar structures in which the same themes were further developed with an ever-increasing subtlety in which overlaid and superimposed pilastrades and dwarf eaves gallery colonnades varied the original formula. The Gordon Street development financed the Gordon Street congregation's new church in St Vincent Street, built in 1857-59, which again must have been intended as an advertisement for their services. Stylistically it marked a further advance drawing upon wider areas of antiquity than Caledonia Road, but in the event it attracted only one further church commission, that for Queen's Park Church, built in a similar but externally less ambitious idiom in 1868-69.

Thomson's widely recognised professional successes in the 1850s were clouded by a series of tragic events at home. In the early years of their marriage Alexander and Jane lived at 3 South Apsley Place in Laurieston. Agnes Elizabeth was born on 24 April 1849, Elizabeth Cooper on 31 January 1851 and Alexander John on 27 November 1852. But Laurieston, although then still a good address, proved vulnerable to the cholera epidemic of 1854 and on 14 March of that year Agnes Elizabeth died. Jane Nicholson, born 8 August 1854, died on 13 February 1855, George born 8 August 1855 survived only until 31 December 1856, and on 3 January 1857 Alexander John died leaving Elizabeth Cooper the only survivor from a family of five. Later in that year the Thomson household moved to Darnley Terrace, a recently completed development he had designed at Shawlands. There on 12 April Amelia was born, followed by Jessie Williamina on 10 April 1858 and the future architect son John on 20 June 1859. In 1861 the Thomsons moved again to Moray Place in Strathbungo, taking the northmost house in a two-storey terrace block built as a speculative venture in association with his measurer John Shields and the builder John McIntyre. Designed in 1859 it was predictably the finest and most original of his earlier terraces, the large end houses being advanced and pedimented with a giant order of pilasters. There Helen was born on 9 July 1861, Catherine Honeyman on 11 February 1863, and Michael Nicholson on 13 October 1864. Peter was born on 19 March 1866, but survived only sixteen days. The size of Alexander Thomson's family seems to have restricted travel. Family holidays were invariably spent in a rented house on Arran. His only recorded trip to London was in 1861 when he visited John James Stevenson, but he may well have made earlier visits. His knowledge of antiquity and of contemporary architecture seems to have been derived from a magnificent library and from the building journals, one of these being the 'British Architect', of which he was one of the founding shareholders in 1874.

In the 1860s the practice was notably prosperous, in large part as a result of the developments undertaken by the accountant Henry Leck, the cab hirer John Ewing Walker and the builder William Henderson who was the client at North Park Terrace (1863-66); 126-138 Sauchiehall Street (1864-66); 249-259 St Vincent Street (1865-67); Grecian Buildings, 252-270 Sauchiehall Street (1868-69); and Great Western Terrace (begun 1869). All of these were built with borrowed money and the practice must have suffered a notable drop in income when Henderson died in May 1870, his property being sequestrated in June. With the practice at a relatively low ebb George Thomson carried out his long-planned intention of becoming a missionary and emigrated to the Cameroons in the Spring of 1871, although he was to remain a partner until 1873.

By 1872 Thomson was in failing health because of asthma and bronchitis, and it was probably because of illness that in February of that year Henry Leck, hitherto a faithful client, commissioned first John Baird and then Peddie & Kinnear to design his building on Gordon Street, replacing an earlier Thomson scheme for a different site which had been stalled by the Caledonian Railway's proposals for Glasgow Central Station. In February 1874 Thomson took Robert Turnbull into a partnership which was backdated to October 1873, probably on account of services rendered since that date. Born in 1839, Turnbull was the son of William Turnbull, joiner and his wife Mary Deans and was more inspector of works than architect, engaged for the 'outdoor' side of the business as correspondence with the Thomson trustees in July 1876 makes clear. But through the family joinery business he did bring new clients in the Lenzie area, for which earlier Thomson villa designs were either reused or adapted. The immediate catalyst for this partnership may have been Thomson's commitment to the Haldane lectures, a series of four delivered in the Spring of 1874. These were a final statement of ideas developed in earlier lectures delivered from 1853 onwards, most of them to the Glasgow Architectural Society and the Glasgow Institute of Architects. These he had co-founded in 1858 and 1868 respectively: he was President of both, the Society in 1861 and the Institute from 1870 to 1872.

In August 1874 Thomson wrote to his brother that 'Mr Turnbull and I are getting on pretty well we are busy with a number of smallish jobs'. But in the winter of 1874-75 his asthma and bronchitis deteriorated and his decision to winter in Italy to regain his health had been left too late. Thereafter he worked mainly at Moray Place and at the time of his death on 22 March 1875 he had been working on a competition design for a town hall. This may have been for Paisley or for Annan, or more probably both: the Annan design is preserved in a relatively coarse presentation perspective made after his death.

In 1897 one of Alexander Thomson's former assistants, William Clunas, put on paper a vivid pen portrait of him at the request of Thomas Ross, together with an indication of what it was like to work in his office. Clunas remembered him as:
'a distinguished looking man of good average height, stout, well and proportionally made, a fine manly countenance with a profuse head of hair. His general appearance was indeed, very much in harmony with the strength and elegance which he imparted to the structures he designed, while the genial smile which so often overspread his face might be fittingly compared to the finished enrichment which was so marked and pleasing a feature of his compositions. …
'In general character he was very unassuming and to those in his employment he was always considerate and even affectionate. By his professional brethren he was held in the highest esteem if one judged from the numbers of the best of them who used to call upon him.
'His pupils were well aware of the great Art Master they were under and experienced the inconveniences as well as the advantages of such a position … for the strictly professional side of business he had little capacity - punctual he was not, neither was he persevering. You could not say he was indolent, but there was a dreamy unrest about him even when engaged on important work which caused matter-of-fact people who were waiting for further details or instructions some annoyance. But when he did plunge in to a piece of work his attitude was that of a real devotee - patient, forceful, and painstaking … While in the mood for work he was apparently urged on by the idea that was moving him … at one time buried in thought, at another wielding the pencil with vigour and precision … His habit in designing was to sketch the work on a small scale on a scrap of paper, and in the course of his cogitations scores of these scraps of paper would be lying rejected about the floor, each with a miniature design that never failed to display the master hand, but to the master himself it was an oft-repeated effort before he was satisfied …
'A notable feature of Mr Thomson's character was his social friendliness. This he displayed in no way more strikingly than the frequent occasions when he had his pupils at his house. He … delighted to speak of examples of antiquity of past ages as well as the more familiar antiquarian lore of his own country. Even ghost and fairies' stories were not beneath his notice.'
There is no record of when Clunas was in the office, but the absence of any reference to George suggests that it was in 1871-73. But it can be read as indicating the importance of George's role as the business manager of the practice and explain why the practice briefly went into relative decline until Turnbull took over its management in the autumn of 1873. Turnbull took a more commercial attitude to style, recycling or adapting Gothic and Romanesque designs of the 1850s if they better met the wishes of his clients. Of Thomson himself Campbell Douglas recalled in 1889:
'In my experience I have only known one man who confined himself to one style, and if his proposed employers insisted on building in a different style, why, then, he let them go elsewhere. That architect was a great man, who probably made less money than some others did, but he left behind him monuments more worthy of his genius.'
Thomson's moveable estate, none of which was inherited, was in fact one of the largest left by any nineteenth-century Glasgow architect at £15,395 5s 6d; he also had substantial property interests.

Alexander was buried in the Southern Necropolis. George came back from the Cameroons to help settle his affairs and marry Isabella Johnston, who returned with him to the Cameroons to help run the missionary hospital he had designed and built in 1874. He died of a fever at Victoria on 14 December 1878.