His grandfather, Archie McLeod, was a professional soccer player with Derry City F.C. in Northern Ireland during the 1930s, and Tennant is a member of the club's supporters.
His father, a retired minister, is a former Moderator of the General Assembly of the Church of Scotland.
As a teenager in the 1980s, wanted to join the actors' union Equity, which already had a person registered with his birth name (David McDonald); he adopted the stage surname Tennant, after Neil Tennant of the Pet Shop Boys.
Cut his acting teeth with Scotland's political 7:84 Theatre Group and had several starring roles with the Royal Shakespeare Company (Romeo and Juliet; As You Like It).