The venue, which is situated round the corner from Shakespeare's Globe, was uncovered in 1988 and now hosts regular productions alongside other events.
It is one of the oldest London theatres and hosted many of Shakespeare's and Marlowe's first productions. Plans are in place to complete the excavation of the Rose and open it to the public permanently.
Broadbent, who recently played Oberon in Filter's A Midsummer Night's Dream, has also been seen in Ghost Stories in the West End and Chekhov in Hell at Soho Theatre.
Speaking to Whatsonstage.com about playing Hamlet, he said: "I’m really excited to be hanging up the Oberon suit and tackling this cut-down, intimate, Nordic Noir-influenced production of Hamlet. The eerie and unique confines of the 50 seat Rose will only add to the audience's experience."
Joining him in the cast will be Suzanne Marie, Liam McKenna and Jamie Sheasby. Director Martin Parr's credits include Romeo and Juliet for the Rose Bankside last year.
Hamlet runs from 7 February to 3 March 2013 (previews from 5 February). Subsequent productions in the Rose season include Dido, Queen of Carthage (6-31 March), Six Characters in Search of an Author (2-14 April) and The Alchemist (6-30 June).