The John Osborne production will see Sir John play legendary patriarch Billy Rice, with Branagh as Archie Rice.
"I am thrilled to be invited to play Billy Rice in this production of what I believe to be one of the great plays of the twentieth century," the actor said.
It will be the final production in Branagh's Plays at the Garrick season.
"This has been a wonderfully successful season for Ken Branagh and his company, and I feel proud and privileged to be joining them," Sir John added.
Set against the backdrop of post-war Britain, the modern classic conjures the seedy glamour of the old music halls for an explosive examination of public masks and private torment.
"I am really looking forward to working on this play. I find The Entertainer riveting and in my opinion there is no better group of actors to bring it to life," director Rob Ashford said.
The Entertainer will play at the Garrick from 20 August to 12 November.
The show will also be broadcast live to cinemas worldwide, on a date to be announced shortly.
Sir John Hurt will return to the London stage for the first time in a decade, to star opposite Sir Kenneth Branagh in The Entertainer.