Buemi was confirmed as Red Bull's back-up driver the 2012 season following Toro Rosso's decision to drop him.
The 23-year-old, who started his Formula One career as a Red Bull test driver in 2008 before spending three seasons at STR, is determined to make the most of his opportunity at the double world champions.
"I was in contact with other teams from December and I had opportunities elsewhere. But ultimately the best solution was to stay with Red Bull," he told Swiss paper Le Matin.
"I will be at the factory often. I will be an integral part of the best team on the grid, and it is obviously very positive. Now it's up to me to do my best in the simulator to prove to them that I am qualified to drive the Red Bull in case Mark Webber's contract is not renewed for 2013."
He admits he did not expect to be dropped by the Faenza-based squad, but says Red Bull quickly made him an offer.
"Obviously, I was surprised as I was not expecting it at all. But the people of Red Bull immediately offered me the job as third driver. I thought about it and I finally agreed," he said.
He added: "The contract I just signed is only for one yar. After that, I have not been promised anything, we'll see. It is very difficult to predict what will happen in 2013 because the contracts of many drivers end after the season.