David Veitch was born in Port of Monteith, Perthshire, Scotland on 13 June 1875. It is thought that he was articled in Stirling as he was living in Stirling whilst attending Glasgow School in 1896-97. In c.1903 he formed the partnership Crawford & Veitch [also known as Andrew Rennie Crawford & Veitch] with his brother-on-law Andrew Rennie Crawford (1874-1933). In 1904 they submitted an entry in a competition to design the Mitchell Library in Glasgow. Their designs are illustrated in British Competitions in Architecture vol. 1, no. 5, September 1905 (pp. 38-39). The partnership was probably dissolved in 1910 as emigrated to Canada that year.
It is not known if Veitch continued to practice as an architect following his move Canada or if he returned to Scotland. He was living in Winnipeg in 1921.