"I congratulated Seb just after the race, but I wanted to repeat my congratulations," Schumacher told his website.

"His fighting spirit throughout the season and the way he played his trump card in the last race is deserving of praise.

"I bow to so much talent, persistence and his science of driving. We have been friends for many years and I am happy for him."

Red Bull's Vettel, 23, won his fifth Grand Prix race of the 2010 season in Abu Dhabi last Sunday to win his first World title by four points from Ferrari's Fernando Alonso.

Having come out of retirement to race for Mercedes this season, the 41-year-old Schumacher had a disappointing return to Formula One as he finished ninth in the drivers' championship.

Vettel and Schumacher will team up next weekend during the Race of Champions to be held in Dusseldorf.

After his first triumph, Vettel has said he has a long way to go to be mentioned in the same breath as Schumacher, despite several comparisons.

"He's a legend and I'm only at the start of my career," said Vettel.