David Rhind was born in Edinburgh in 1808, the son of John Rhind and his wife Marion Anderson. His father was cashier to the Edinburgh Friendly Insurance Company, and had significant legal and professional connections. David's choice of architecture may not have been looked upon favourably as he did not begin his training until after the death of his father. He then became a pupil of George Smith, one of William Burn's former clerks in 1827, 1828 or 1829, according to a letter written by Burn to the Duke of Buccleuch in 1836. He then trained in London, apparently in the drawing office of Augustus Charles Pugin. While there he became friends with Charles Barry. Thereafter he completed his training by travelling in Italy, perhaps upon Barry's recommendation.
Rhind began practice in Edinburgh in 1828 from his mother's house on Forres Street. His first commissions were from the Commercial Bank, probably through family connections there. James Gillespie Graham, hitherto the bank architect and a friend of the younger Pugin, may have helped Rhind earn these early commissions, although Gillespie Graham's precarious financial position makes that somewhat unlikely. During this period Rhind entered the competition for rebuilding the Houses of Parliament; the design was not premiated and unfortunately no longer exists. Later in the 1830s Rhind entered and won the competition for the Scott Monument in Glasgow. This led him to meet the sculptor Handyside Ritchie, who influenced his use of sculptural ornament in his architecture and executed the sculpture of many further commissions.
Rhind's use of sculpture came into fruition with his first major commission, the Head Office of the Commercial Bank of Scotland in George Street, Edinburgh in 1843, where he was given relatively free rein to design a bank which would eclipse those of the Bank of Scotland and the Royal Bank of Scotland. Rhind organised a commission for the pedimental sculpture. James Wyatt won the competition and Handyside Ritchie executed the deeply undercut figures. Rhind thereafter became architect to the bank, designing virtually all its branch offices, many of which were to reflect the opulence of the head office. The most ambitious of these branch offices was that in Glasgow, a Roman palazzo style design from 1854, but nearly all of the branch offices in smaller towns had real distinction in an astylar palazzo form as at Perth, Hawick and Jedburgh, the earlier ones being very similar to those designed by his pupil John Dick Peddie for the Royal Bank.
Rhind's success at the Head Office on George Street led to his appointment as architect to the Trustees of Daniel Stewart, but here he had a difficult time producing a satisfactory design within budget. Rhind was also appointed architect to the Life Association of Scotland, probably through family connections. His commission to provide them a new head office by combining two existing buildings on Princes Street became a public controversy; Rhind found it impossible to stick to instructions or budget, and drawings in the DPM Collection at RCAHMS show that John Dick Peddie was involved in some of the earlier schemes. Finally he produced an elaborate design for a Venetian High Renaissance palazzo which required the destruction of most of the existing premises. At Rhind's suggestion, Sir Charles Barry was consulted in London for an opinion, and Rhind's consequent instructions were to redesign the ground floor according to Barry's design to accommodate more shop space, and combine it with his original elevation which was modified to accommodate mezzanines. The commission was ultimately damaging to Rhind's reputation, in part due to structural problems because retained internal walls proved unable to support the new structure.
Nonetheless, Rhind remained a prominent designer of commercial buildings and was active in professional organizations. In 1836, Rhind was elected to the Royal Society of Edinburgh and contributed to the Society for the Promotion of the Fine Arts in Scotland. He was an active Mason. By 1840 he was a founding member and treasurer of the Institute of Architects in Scotland, and in 1855 he became the first architect to be elected President of the Scottish Society of Arts. He was also a member of the Established Church and an elder of St Andrew's Church on George Street. This connection perhaps influenced his appointment in 1860 as architect to the General Assembly of the Church in Scotland, for whom he skillfully extended the Assembly's meeting hall and built the Normal School on Chambers Street.
Although his official position remains unclear, Rhind also served as an architect to the Prison Board, and built many Sheriff Court houses. He seems to have again earned this position on account of family connections, his brother McDuff Rhind being a sheriff. His courthouse designs were stylistically varied, relying more on baronial traditions than the Commercial Bank branch offices. Again, in Oban, he underestimated the building costs and legal opinion had to be sought.
Rhind was never a prolific domestic architect, though he showed an interest in bold, sculptural Scots Baronial, as best exemplified in Carlowrie Castle in 1851-52, similar in style to his courthouses at Dumfries and Selkirk.
Rhind married Emily Shoubridge who died in 1840, when she was only twenty-eight. He married again in 1845, to Mary Jane Sackville-Pearson and started a second family. He was survived by eight children: Lucy, Agnes, Emily, Marion Alicia, Edith, Ernest Sackville, Williamson, and David Edward. As many as five more may have died in infancy. He retired as late as 1882, and died at 12 Selwood Terrace, Onslow Gardens, London on 26 April 1883. He left moveable estate of £359 13s 0d + £279 10s 2d. His obituarist reports that 'he was much respected by his professional brethren, many of whom, now occupying grand positions in the city, passed through his office'. His pupils included Robert Morham and Hippolyte Jean Blanc as well as Peddie.