The son of the actor and theatre manager and owner James Burbage, Richard had attained wide popularity as an actor by age 20. He was a member of the Earl of Leicester's company (Earl of Leicester's Men) and remained with it through its evolution into the King's Men in 1603. He also prospered as a major shareholder in the Globe (Globe Theatre) and Blackfriars (Blackfriars Theatre) theatres. Excelling in tragedy, Burbage was much in demand on the stage and performed in works by Thomas Kyd, Ben Jonson, and John Webster, as well as by Shakespeare.

Although short and stout, Burbage was apparently an impressive figure, and there are numerous praises of him in contemporary prose, verse, and plays. Burbage was a painter as well; a painting of a woman at Dulwich College, London, is undoubtedly by him, and the Chandos portrait of Shakespeare (Shakespeare, William) has sometimes been attributed to him. Shakespeare was closely associated with him during his career in London and in his will left Burbage a token remembrance.