Vettel dominated Formula One this season as he claimed a record-breaking 15 pole positions and 11 grands prix victories on his way to his second world title.
The Red Bull racer, who is the sport's youngest double world champion, had been competing in the Race of Champions in Dussledorf but arrived in London in time to collect his award.
"I don't know where to start to be honest. Last year was my first time picking up one of these trophies, and it means a lot," Vettel said.
"I felt very honoured when I walked down the stairs and everyone, including lots of past and present racing drivers, were clapping, giving me appreciation and respect for what I have achieved. It made me feel very special.
"For all of us, when we started racing as a kid and dreaming about F1, it was so far away. You see those guys and they're like heroes, you dream about one day and then it gets closer and closer.
"My biggest dream was to win the World Championship once, and [when I did] it took a long time to sink in - you have proved yourself, and you have something no one can take away.
"It's difficult to realise what we have achieved [this year], with so many races, wins, poles - sorry Nigel [Mansell]. F1 means a lot: I love the racing, the cars, the history, and when people come and remind you of this it's fantastic."
The 24-year-old's Red Bull RB7 was also honoured, winning the award for Racing Car of the Year, having taken Vettel and team-mate Mark Webber to 12 race wins and 18 pole positions.
Design guru Adrian Newey was on hand to collect the award, joined by chief designer Rob Marshall, head of race engineering Ian Morgan and chief engineer Mark Ellis.
"Last year we produced a good car but made it very difficult for ourselves," said Newey. "This year out of the blocks from the start, the car was competitive right away and we just managed to keep it there, and that's a credit to everyone.
"Some of the races have been very close and it's a tribute to the team and drivers that we've stayed there."
There were other awards for Formula One with Jenson Button winning the British Competition Driver of the Year Award and Force India's Paul di Resta crowned Rookie of the Year.
"It's been a tough year," di Resta told Autosport. "But it's been an incredible journey.
"Force India gave me the opportunity two years ago to drive their car the first time and to help them to their best year, sixth in the Constructors' Championship, is great.
"My personal highlight was qualifying for the British Grand Prix, when we started sixth. The race didn't go quite so well, but there you go."