Hamilton was born in Britain in 1767. He began his naval career at the age of nine on his father's ship, the Hector. He attended the Royal Naval Academy at Portsmouth from 1777 to 1779. He commanded a number of vessels in the Royal Navy and was also a member of the British parliament several times between 1790 and 1812 while still serving in the Royal Navy. He became baronet of Trebinshun on his father's death in 1784. From 1814 to 1817, he was Lieutenant Governor of Heligoland. Hamilton was made an admiral on 22 July 1830, and died at the family home at Iping, West Sussex in 1849.