The new arrangement will continue until 2018, with the BBC showing half of the races live. Sky Sports will broadcast coverage of all practice sessions, qualifying and every race.
Barbara Slater, director of BBC Sport, said: "We are absolutely delighted that F1 will remain on the BBC. The sport has never been more popular with TV audiences at a ten-year high and the BBC has always stated its commitment to the big national sporting moments.
"With this new deal not only have we delivered significant savings but we have also ensured that through our live and extended highlights coverage all the action continues to be available to licence-fee payers."
The BBC will broadcast races including the Monaco grand prix, British grand prix and the final race of the season, in addition to practice and qualifying sessions from the races it has the rights to show live.
It will also carry highlights of any grand prix that it does not show in full.
Sky Sports' managing director Barney Francis said that the announcement was "fantastic news for F1 fans" and promised to "give F1 the full Sky Sports treatment, with a commitment to each race never seen before on UK television".
BBC Radio 5 Live will have live commentary of all races and both broadcasters will provide extended coverage across online, 'red button' services and mobile platforms.
Both broadcasters will also provide build-up coverage before each race on Sky News, Sky Sports News and the BBC News channel.
The BBC has had exclusive UK rights to Formula 1 coverage since 2009. F1 supremo Bernie Ecclestone and McLaren team principal Martin Whitmarsh had both encouraged the BBC to keep broadcasting grands prix.
> BBC to air 2011 F1 season in HD