He was born in Glasgow in 1756, the only son of John Campbell of Clathick, Perthshire, Lord Provost of Glasgow 1788/90, and Agnes Colquhoun, the only child of Laurence Colquhoun of Killermont, Dumbartonshire. On succeeding to the estate of Killermont upon the death of his father in 1804, he assumed the additional surname and arms of Colquhoun.
On the downfall of the ministry of All the Talents, he was appointed Lord Advocate on 28 March 1807. At this time, most of the Scotch patronage was in the hands of the Dundas family, and William Erskine, Alexander Maconochie. and Henry Cockburn were actually chosen deputes by Lord Melville before Colquhoun had received the appointment.
In the following May, he was returned as Member of Parliament for the Elgin district of burghs, but after three years resigned his seat. In July 1810 he was elected member for Dumbartonshire, which county he continued to represent until his death in 1820.
Colquhoun, as the Lord Advocate, took part in reforming the constitution of the Court of Session, and was appointed one of the thirteen commissioners who sat for the first time on 30 November 1808 for the purpose of inquiring into the administration of justice in Scotland. The correspondence between him and Erskine, the late lord advocate, on the subject of the respective merits of Lord Grenville's and Lord Eldon's bills for the reform of legal procedure will be found in the 'Scots Magazine' for 1808, pp. 70–2, 149–52. On the death of Lord Frederick Campbell, Colquhoun was appointed Lord Clerk Register, on 4 July 1816, much to the disappointment of Erskine's friends, who had hoped that the post would have been offered to him. He was a partner in the Thistle Bank of Glasgow, of which his father was co-founder.
Colquhoun died on 8 December 1820, after an illness of a few days, at the house of his son-in-law, Walter Long, at Hartham, Wiltshire, and was buried in the parish churchyard of New Kilpatrick near Glasgow. 
In 1796 he married Mary Ann, daughter of the Rev. William Erskine, episcopalian minister at Muthill, Perthshire, and sister of William Erskine, afterwards Lord Kinneder. His wife survived him for many years, and died at Rothesay on 15 May 1833. 
They had six daughters and two sons:
- John Campbell Colquhoun of Killermont and Garscadden,
- William Laurence Colquhoun, who died on 16 Jan. 1861.
Their eldest child died within a year of her birth, and it was on this occasion that Carolina Oliphant, afterwards Baroness Nairne, wrote The Land of the Leal, which she sent to her old friend Mrs. Colquhoun.
Colquhoun was a good classical scholar, a sound lawyer, and an eloquent pleader. Being a man of independent fortune and of reserved manners, he hardly took the position at the bar to which his abilities entitled him. His only reported speech does not appear to have been a great success. He rose 'amidst a tumultuous cry of Question! Question!' to take part in the debate on the Duke of York's conduct, and had not got very far when the house became 'so clamorous for the question that the hon. member could no longer be heard'.
- "Church registers - Old Parish Registers Births and baptisms - Search results". Scotland's People. National Records of Scotland and the Court of the Lord Lyon.
- History of the Speculative Society of Society of Edinburgh. Speculative Society of Edinburgh. 1845. p. 138.
- Barker 1887.
- "Archibald Colquhoun was Campbell of Clathwick". UCL Department of History. Retrieved 19 October 2017.
- "Thistle Bank Company - Archives Hub".
This article incorporates text from a publication now in the public domain: Barker, George Fisher Russell (1887). "Colquhoun, Archibald Campbell-". In Stephen, Leslie (ed.). Dictionary of National Biography. 11. London: Smith, Elder & Co.