The deal, which involves a tie-up between the BBC's commercial wing, BBC Worldwide, and Two Way TV, backed by cable company NTL, is the first time BBC programmes have been licensed as commercial games.
Interactive channel Two Way TV, which has licensed the rights from the BBC, will host the new format.
Viewers will be able to play against each other as contestants in the shows and then compare scores with their neighbours.
For example, up to four viewers in a household playing Mastermind will be able to pick their own specialist subjects, with scores registered and compared against other households taking part.
In addition to quiz shows the BBC has licensed the interactive rights to Antiques Roadshow and Film 2000.
BBC first
The deal, which involves a tie-up between the BBC's commercial wing, BBC Worldwide, and Two Way TV, backed by cable company NTL, is the first time BBC programmes have been licensed as commercial games.
Drew Kaza, head of the BBC Worldwide's internet and interactive unit, said the arrangement would be worth "thousands of pounds" to the BBC.
Two Way TV's Matthew Tims said he hoped the programmes would make some of the channels most popular games.
"This is a prestigious package of instantly recognisable BBC programmes," he said.
As it develops the format Two Way TV eventually plans to synchronise interactive TV games with broadcast television.
Two Way TV has also struck deals for the interactive rights to Pathé's archive of early news footage, and the Channel 4 quiz programme, Crystal Maze.