Davison was born Peter Moffett in London, but chose the stage name of Peter Davison because the name, Peter Moffett, was already being used by another actor. Peter Davison's father was an electrical engineer who was originally from Guyana. Peter Davison studied at the Central School of Speech and Drama, and appeared in several stage productions and some minor television roles before he got his big break in 1978. His performance as the ne'er-do-well Tristan Farnon in All Creatures Great and Small made him a household name. He married American actress Sandra Dickinson in the same year, but they eventually divorced in 1994. He and Dickinson had previously appeared together in an episode of the television series The Tomorrow People (1975) and together composed and performed the theme tune to Button Moon, a children's programme broadcast in the 1980s. He made a cameo appearance alongside Dickinson as the Dish of the Day in the television version of The Hitchhiker's Guide to the Galaxy (1981), whose producers considered it humorous for an actor known for playing a veterinary surgeon to appear as a cow. Davison also appeared in some British sitcoms, including Holding the Fort, Sink or Swim and Ain't Misbehavin', as well as appearing in dramatic roles.

In 1981, Davison signed a contract to play the Doctor for three years, succeeding Tom Baker (the Fourth Doctor). Attracting such a high-profile actor was as much of a coup for the programme's producers as getting the role was for him, but he did not renew his contract because he feared being typecast. Reportedly, Patrick Troughton (who had played the Second Doctor) had recommended to Davison that he leave the role after three years, and Davison followed his advice.

It was not until 1986 that Davison worked on another very popular series. He played Dr Stephen Daker, the ingenuous hero of A Very Peculiar Practice, written by Andrew Davies. The surreal comedy-drama was revived several years later as A Very Polish Practice. Davison also played the lead in Campion, a series based on the period whodunnits of Margery Allingham. This, and the opportunity to play Tristan Farnon again in 1985 and 1990, kept Davison busy until the early 1990s, when he gradually faded from the public eye. He continued to appear occasionally on television, including playing the lead in Harnessing Peacocks in 1992 and an appearance on the American show Magnum, P.I., but it was not until 2000 that he returned in another major role, that of David Braithwaite in At Home with the Braithwaites.

During the 1990s, Davison appeared in several radio series including Change at Oglethorpe in 1995 and Minor Adjustment in 1996. In 1998 he appeared in the BBC Radio 4 comedy drama series King Street Junior. In this, he played a teacher, but he left after only one series and was replaced in the role by Karl Howman. In 1999 he appeared as the outgoing headteacher in the television series Hope And Glory. He has also starred in the television series The Last Detective (2003-date) and Distant Shores (2005) for ITV, the latter where he coincidentally also played a doctor.

Davison returned to play the Doctor in the 1993 charity special Dimensions in Time. He has also reprised the role in a series of audio plays by Big Finish Productions.

Davison made a guest appearance in the first episode of the second series of the BBC Radio 4 science fiction comedy series Nebulous, broadcast in April 2006.

Davison's daughter with Dickinson, Georgia Moffett, is also an actress, and auditioned for the role of Rose Tyler, the current companion of the Ninth and Tenth Doctors. Peter Davison has two other children with his present wife, Elizabeth Morton.