Richards was team boss at BAR and Benetton
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David Richards' Prodrive outfit will line up alongside the 11 existing teams in the 2008 Formula One championship.
The decision by world governing body the FIA means Richards, a former BAR and Benetton team boss, will return to the grid for the first time since 2004.
As expected, all 11 current teams, including recent newcomers Super Aguri, are included on the 12-team entry list.
Ex-Minardi boss Paul Stoddart, Eddie Jordan and BAR co-founder Craig Pollock were among the 10 rejected bids.
Richards also runs Subaru's World Rally team and that, coupled with his previous experience in F1, helped swing the decision in his favour.
"Prodrive have the best combination of financial backing, technical capability and motorsport experience," said FIA president Max Mosley.
"The team are well known to the FIA through their participation in the World Rally Championship and Richards has experience as a Formula One team principal."
Richards left BAR at the end of 2004 after Honda increased their stake in the team and is now delighted to be back in the sport.
"This is wonderful news for everyone in the company," said Richards, who is seeking planning permission for a new Banbury-based factory.
"We always wanted to be in Formula One with our own Prodrive team and now we are one step closer.
"We now have less than two years to build a team and put two competitive cars on the starting grid. The task is enormous but we relish the challenge."
The FIA world council made the final decision on which teams would be given the nod for the 2008 campaign.
But Mosley said it was never an option to drop any of the existing teams, which means unproven Japanese newcomers Super Aguri retain their place.
The decision comes as a major disappointment not only to Stoddart and Jordan, who sold their teams last season, but Carlin Motorsport and Jean Alesi's Direxiv outfit, whose bids were very developed.
It is unlikely that they will get a chance in the near future to enter the F1 fray as Mosley ruled out further expansion.
"The limit of 12 teams was imposed for safety reasons and circuit facilities," said Mosley. "So, the number is unlikely to increase."