The team behind the first theatre to be built in London for 30 years hopes it will help foster a New York-style "off Broadway" scene in the capital.
The £7m St James Theatre, which has no public subsidy, will cater to an audience of just over 300 in its main auditorium and has a studio theatre with a capacity of 100.
Robert Mackintosh, the venue's joint chief executive and creative director, said he had backed the project because he felt London lacked commercial theatres catering for audiences of fewer than 500 people.
David Gilmore, the artistic director, said: "London has never been like New York and had a strong off-Broadway presence, where commercial shows could be tried out. If they are successful they move up, if they aren't no one loses their shirt."
The first play to open at the new venue is Bully Boy, written by Sandi Toksvig, which is about moral issues of military occupation and starts on Tuesday. It will be followed by Daddy Long Legs, a musical based on Jean Webster's novel, written and directed by John Caird, a co-director of Les Misérables.
To celebrate the opening, a party was held at the venue in Victoria last night, with an opening address given by Evgeny Lebedev, chairman of the group that owns The Independent.
"The fact Robert Mackintosh and his team could finance such an ambitious project is a great testament to Britain's love of culture," he said.
"It's an extraordinary feat to open a theatre in such times. It has risen like a phoenix from the ashes of the Westminster Theatre.
"I grew up in the Soviet Union, where after the Revolution theatres sprang up like mushrooms – it is always a great source of joy when a new theatre opens in my favourite city."
While the site is not in London's West End "theatreland" district, stretching from Piccadilly to Aldwych, it is only a few minutes' walk away from two of the biggest shows in London: Billy Elliot and Wicked.
St James Theatre was built on the site of the Westminster Theatre, which was demolished after being badly damaged by fire in 2002. "The whole area is undergoing a huge transformation," Mr Gilmore said, predicting that Victoria will become more popular as an entertainment destination.
He was brought in a year ago as artistic director. "I was attracted to the idea," he said. "How often does any artistic director get to open a new building, especially about 50 yards from Buckingham Palace?"
Another new theatre is planned for London, although building is not expected to start until 2017. Nimax, which operates five venues in London, has a site close to Tottenham Court Road.