Stewart will next play the tramp Vladimir in Waiting for Godot
Stewart landed best supporting actor for the Royal Shakespeare Company production, which starred David Tennant in the title role.
The Oliviers are presented by The Society of London Theatre to honour the best West End stage productions.
They were first held in 1976 and became known as the Olivier Awards in 1984 when actor Sir Laurence Olivier agreed to them being named after him.
