St James Theatre in Palace Street, Victoria, was built on the site of the former Westminster Theatre which was destroyed by a fire in 2002.
The owners hope the Â£7m complex will attract new audiences and help foster commercial theatre outside the West End.
Bully Boy, a play by comedienne Sandi Toksvig, launches the debut season.
Originally a chapel in 1766, the building was then altered so it could be used as a cinema in 1924 and subsequently converted into a theatre in 1931.
For many years it was owned by the Moral Re-Armament movement which used it to present shows with a moral or spiritual message.
The new complex has a 312-seat main house and a studio space capable of accommodating up to 150 people as well as apartments.
The theatre will be fitted with multi-media broadcast facilities that will be used to show performances on the venue's own BSkyB satellite channel.
For the first time in 30 years a new theatre has opened to the public in London's West End.