Jacobi, an only child, was born in Leytonstone, London, England, His family was working class. In his teens he went to the Leyton County High School and became an integral part of the drama club, The Players of Leyton.
At 18, he won a scholarship to the University of Cambridge, where he read history at St John's College and earned his degree.
A "forceful, commanding stage presence", Jacobi has enjoyed a highly successful stage career, appearing in such stage productions as Hamlet, Uncle Vanya, and Oedipus the King.
He received a Tony Award for his performance in Much Ado About Nothing. His stage work also included playing Edward II, Octavius Caesar, Richard III, and Cyrano de Bergerac.
Though principally a stage actor, Jacobi has appeared in a number of films, such as Henry V (1989), Dead Again (1991), Gladiator (2000), Gosford Park (2001), The Golden Compass (2007), The King's Speech (2010), My Week with Marilyn (2011), and the forthcoming Hippie Hippie Shake.
In March 2006, he registered his civil partnership with Richard Clifford, four months after civil partnerships were introduced in the United Kingdom. They live in north London.
He was invited to perform the role at Kronborg Castle, Denmark, better known as Elsinore Castle, the setting of the play. In 1978 he played in the BBC Television Shakespeare production of Richard II, with Sir John Gielgud and Dame Wendy Hiller.