Born and raised in Edinburgh, Charleson attended the Royal High School and then went on to attend Edinburgh University. He initially studied architecture but switched to an MA degree after cultivating an interest in acting. He won a place at the London Academy of Music and Dramatic Art after graduating from Edinburgh.

In preparing for his role of Eric Liddell, the religious Olympic runner, in the film Chariots of Fire (1981), Charleson read the Bible from beginning to end.

He died in London, from AIDS related complitions, while playing Hamlet in Richard Eyre's production at the Olivier. Sir Ian McKellen said that Charleson played Hamlet so well it was as if he had rehearsed the role all his life.

His name was used posthumously for the Ian Charleson Awards, which have been presented annually since 1991 to reward the best classical stage performances by actors aged under 30.