Hamilton first came to notice while performing at the Edinburgh Festival Fringe in the 1970s. In the mid-1970s he sustained himself by taking jobs at Harrods and the Post Office before joining the BBC in 1976.
Since 1995, Hamilton has written and played the lead role of Satan in the Radio 4 sitcom Old Harry's Game. He toured with his UK stand-up show Hat of Doom in 2008.
On 16 March 2007, he co-presented BBC Radio 4's Woman's Hour programme alongside usual presenter Martha Kearney as part of that day's Comic Relief fundraising activities, after defeating Richard Hammond and Kelvin MacKenzie in a poll.
In 2009, Hamilton presented the BBC Four series It's Only a Theory with Reginald D. Hunter.
Hamilton is 5 feet 2 inches (1.57 m) tall. He has no thumb on his right hand. He joked that it was amputated when he was five "by a surgeon who felt that symmetry was over-rated" to the audience of 'Andy Hamilton Sort of Remembers' on Radio 4 in October 2017.