The Gala took place at the Ciragan Palace in Istanbul, overlooking the Bosporus River. Fernando Alonso and Kimi Raikkonen were also present to pick up their trophies for finishing second and third in the championship.
Vettel was presented with his award by FIA president Jean Todt.
"It’s a fantastic feeling to be able to take this trophy back home for another year. As I said last time, it isn’t something you want to give back," said Vettel.
"Winning the title with Red Bull Racing three times in a row makes us all feel very proud. This was a season with lots of ups and downs and the team had to push hard to get me over the line. In the garage and at the factory everyone did an incredible job, and the support we had from Renault was also great."
Vettel won five races on his way to becoming the youngest ever triple world champion at the age of 25. His team, Red Bull Racing, also collected the Constructors Championship, which they secured in the United States Grand Prix.
"This is a phenomenal achievement for our team," said Christian Horner, team principal of Red Bull Racing since their creation in 2005.
"The hard work and the dedication this year have been exemplary - but I think hard work and dedication have been common up and down the pit lane in this fantastic Formula One season. It didn’t seem possible we could raise our game after last year but I think we have. The team have used every scrap of their skill and ingenuity, they’ve had the courage of their convictions and have refused to buckle under the most enormous pressure. I’m honoured to collect this trophy on their behalf".