Webber, who claimed the ninth victory of his Formula One career on Sunday in the British Grand Prix at Silverstone, had been linked with a move to Ferrari.
But the 35-year-old, who trails Ferrari's Fernando Alonso by 13 points in the overall standings, has opted to remain with Red Bull for a seventh season.
Red Bull driver Mark Webber. Photo: AFP
"I've been with Red Bull Racing since 2007 and have achieved nine grand prix wins during that time," said Webber.
"I'm high on confidence at the moment and firing on all cylinders.
"I know the team well and I'm very comfortable here. We have grown together over the years and it feels like absolutely the right thing to stay with Red Bull for another season.
"The team is constantly working hard to improve in all areas and we've shown that together we can win races.
"It's great to be able to make this announcement off the back of the win in Silverstone at the weekend and I'm looking forward to competing on the edge and pushing myself in every race again next season."
Team chief Christian Horner added: "Mark has driven very well in the first nine races of this season and his performance has been impressive.
"Much of his Formula One success has been during his time with Red Bull Racing and together we have achieved 10 poles, nine wins and 31 podiums.
"As there was a strong desire from both sides to continue the partnership, it was a logical decision to extend our relationship and it is with great pleasure we confirm Mark will drive for us in 2013."
With defending double world champion team-mate Sebastian Vettel of Germany already contracted to Red Bull Racing until the end of 2014, the English-based stable are the first team to confirm their 2013 driver line-up.
Asked if 2013 would be his last season in F1, Webber replied: "I've been asked this question for the past four years and my answer remains the same.
"It's a results-based sport at the front of the grid so the future lies in my own hands. It's down to me to deliver the on-track results."