Audiences will be able to see James, a real-life smoker, perform from Tuesday next week until 23 September.
He will star alongside former EastEnder Shane Richie in two dramas by James McLure.
In Lone Star, set in a redneck Texan town, Jagger plays a smalltown simpleton; and in Private Wars he plays a poetic East Coast aristocrat recovering from injury in an army hospital.
An insider said: "When he was first cast we thought he'd be like his mum and dad - not much cop at acting. But apparently he is fantastic. He has blown the producers away."
It is Jagger's first professional theatre role and only his second adult acting job.
He has just finished filming a small part in Knife Edge, a classic English horror starring Dame Joan Plowright, Nathalie Press and Hugh Bonneville.
Jagger has previously dabbled in modelling, following in the footsteps of mother Jerry Hall and his sister Lizzy, 23.