Parker, who played Clive Healey in the 1992 Whitney Houston film, will lead the Swan Theatre cast in Stratford-upon-Avon, England when Wolf Hall and Bring Up the Bodies premiere back to back in December (13).
Mantel's historical novels won the Man Booker Prize in 2009 and 2012. The books have been adapted for the stage by Mike Poulton.
Lucy Briers will double up as Katherine of Aragon and Jane Boleyn, while Leah Brotherhead will portray Jane Seymour and Princess Mary, and Nicholas Day has been cast as the Duke of Norfolk.
The two projects will run at the Swan Theatre from 11 December (13) to 29 March (14).