The 23-year-old Red Bull driver led from pole to chequered flag under the Yas Marina floodlights to chalk up his fifth win of the season.
Alonso, the pre-race favourite for a third title, struggled home seventh after his team made the wrong call on strategy and left him following Renault’s Russian rookie Vitaly Petrov for 40 agonising laps.
Vettel, adding the drivers’ crown to the constructors’ championship his team won the previous weekend in Brazil, finished with 256 points to Alonso’s 252 after winning in Abu Dhabi for the second year in a row.
“We have only led this championship once and when it mattered. I am speechless,” said the youngster.
He had started the day 15 points behind Alonso, with much of the build-up dominated by speculation about whether he would allow Australian team mate Mark Webber to pass for the title.
In the end, Webber finished eighth and was third overall.
“Thank you boys, unbelievable,” gasped Vettel over the team radio, the tears flowing behind the visor after he took the chequered flag.
Team principal Christian Horner and owner Dietrich Mateschitz, bursting with pride, spared him no emotion.
“You are the world champion. Enjoy it. You are the man,” Horner bellowed from the pit wall.
“I love you,” answered Vettel.
Petrov unpassable
Alonso, wished good luck by King Juan Carlos on the starting grid, paid the price for an early pitstop that dropped him to 13th.
“Afterwards it was really clear it was a mistake,” said Ferrari team boss Stefano Domenicali, without saying who had made the call.
“What I feel inside is a lot of pain…for sure it was the worst race of the year for us and that’s why it hits you very hard in the head.”
Vettel, asked jokingly whether he might be Petrov’s main sponsor next year, thanked the Russian, whose future in the sport remains uncertain.
Webber had been the first of the contenders to pit, triggering Alonso’s fateful decision to follow him in to keep him covered, and he also became bogged down in traffic.
“He’s down really, to be honest with you,” Webber’s father Alan told Reuters, watching from a distance as team members partied away.
“He fired the arrow and he was aiming for the target way up there and he missed the target and that’s taking a long time to come back down to earth.”
Hamilton second
McLaren’s Lewis Hamilton, the previous youngest champion who had to win in Abu Dhabi to have any hope of a second title, finished second on the night with team mate and outgoing world champion Jenson Button third.
While Vettel celebrated, seven-times world champion Michael Schumacher’s comeback season ended with a smash on the opening lap when his Mercedes spun and was speared by Force India’s Italian Vitantonio Liuzzi.
The great, who last stood on the podium as a Ferrari driver in 2006 and is the only other driver to have won the title for Germany, was fortunate to escape serious injury as the car ploughed into the stationary Mercedes and rode up over the airbox just behind Schumacher’s head.
The safety car was then deployed for four laps.
