The Red Bull driver, 26, won the final race in Brazil to equal a record of nine consecutive F1 victories set by Alberto Ascari between 1952-53.
He also matched Michael Schumacher's record of 13 wins in a single season.
German Vettel joins legends Juan Manuel Fangio, Alain Prost and Schumacher as a four-time champion.
It is the first time Vettel, who made his Formula 1 debut in 2007, has been given the BBC honour.
"Thank you very much for the award," said Vettel, who did not attend the awards ceremony in Leeds. "It's something very special if I look at the list of previous winners.
"It's been a fantastic year."
The 10 races before the summer break saw five different drivers - Kimi Raikkonen, Fernando Alonso, Nico Rosberg, Lewis Hamilton and Vettel - take victory.
But on resumption, Vettel won every single race - nine in total - to move his career victory tally to 39. That moved him up to fourth on the all-time lists with only Schumacher, Prost and Ayrton Senna ahead.
After winning the title at the Indian Grand Prix, with four races to spare, Vettel said: "I'm speechless. I don't know what to say, I crossed the line and I was just empty.
"You want to think of something to say and I just can't. It has been an amazing season, the spirit in the team is great."
Vettel celebrated his title win with a series of perfect 'doughnut' spins on the start-finish straight.