The award, chosen by public vote, capped a 2010 for McCoy, British National Hunt (jump) racing's most successful jockey of all-time and the champion rider for the last 15 years, that finally saw him win the Grand National, the sport's most famous race, on Don't Push It.
The 36-year-old Northern Irishman succeeded Manchester United and Wales footballer Ryan Giggs as the winner of an award restricted to UK sportsmen and women that was first presented in 1954.
Multiple darts world champion Phil Taylor was the runner-up and European heptathlon champion Jessica Ennis third in the poll.
"This is an unbelievable feeling standing here in front of all these amazing people," McCoy said. "To win this award is very surreal.
"When I started off as a jockey I wanted to be champion jockey in my mind, and I have been lucky enough to be champion jockey for 15 years.
"But the Grand National is the biggest horse race in the world and everyone knows I had won all the other races and to finally achieve that... it was just an unbelievable day."
McCoy's friend and rival jockey Ruby Walsh added: "He's dominated racing like Tiger Woods dominated golf and Roger Federer dominated tennis."
Europe's victorious Ryder Cup golf team that defeated the United States at Celtic Manor, Wales, in October to regain the trophy won the team of the year award, with their captain, Colin Montgomerie, named coach of the year.
"We were very fortunate and we had unsung heroes in our caddies and we want to thank every spectator who turned out in support of the European team in Wales," said Montgomerie.
Spain's Rafael Nadal, who won three (the French Open, Wimbledon and US Open titles) out of a possible four grand slam tennis tournaments in 2010, was chosen as the overseas sports personality of the year.
Meanwhile England footballer David Beckham was given a 'lifetime achievement' award from the BBC.
The former Manchester United, Real Madrid and AC Milan midfielder, who now plays for US Major League Soccer side LA Galaxy, was given the award despite being aged just 35.
Beckham, given a standing ovation that lasted more than two minutes, received his trophy from Manchester United great and 1966 England World Cup winner Sir Bobby Charlton, who himself won the same award two years ago.
As his wife Victoria and sons Brooklyn, Romeo and Cruz looked on, a clearly moved Beckham said: "I'm really humbled to receive an award for something I have always loved and continue to love doing.
"Football is a team game and without the team and the players' support and skill I wouldn't be here today."
He also paid tribute to his former boss Sir Alex Ferguson, still United's manager, by saying: "He's the best manager in football, I regard him as a father figure."
Beckham dedicated his award to British troops serving in Afghanistan, after visiting Camp Bastion on a morale-raising trip in May.
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