Archibald Hamilton was the eldest son of James, 5th Duke of Hamilton, by his third wife, Anne Spencer. His half-brother was James, 6th Duke, whose two sons (Archibald's nephews) James George and Douglas succeeded him as 7th and 8th Dukes, respectively. When Douglas Hamilton died without children, Archibald succeeded him as 9th Duke. On 25 May 1765 Archibald married Harriet [d. 1788], daughter of the 6th Earl of Galloway. They had two sons and three daughters; the eldest son, Alexander, succeeded his father as 10th Duke of Hamilton and 7th Duke of Brandon. Archibald Hamilton served as a Member of Parliament for county Lancaster in 1768.