Rage's managing director, Paul Finnegan, said the footballer is "excited" about being involved.
He will also have a hand in the concept and development of the games, the first of which will be on sale in time for Christmas.
The games will be made for a number of platforms including the Sony PlayStation and Nintendo Game Boy by Liverpool-based software company Rage.
Rage's managing director, Paul Finnegan, said the footballer is "excited" about being involved.
"He hopes to come in and put his slant on how it should work," he said.
"They've looked at the product and they like the product. David's very enthusiastic about it and wants to help."
The game will be an arcade-style game based on one of Rage's existing football products, and the player will be able to control a number of players including Beckham.
They will be the footballer's only officially-endorsed games.
Versions for the Playstation 2 and Microsoft X-Box will be available from spring 2002.
'Sensible'
Mr Finnegan - who is an Everton fan - said: "I just think he's one of the best footballers in the world. If you looked at the papers at the weekend the coverage that David Beckham got is incredible. We're delighted to get him on board."
Finnegan would not reveal how much Beckham will be paid for the three-year deal, but described the sum as "sensible".
The Manchester United star has already signed a £1m deal to promote sunglasses by the designers Police.
The games form a part of Rage's push to drive up profits by signing high-profile names.
The company announced an £8m pre-tax loss in the second half of 2000.
They already produce the Jonah Lomu Rugby game and recently announced a deal with world champion inline skaters Cesar Mora and Fabiola da Silva.