"I'm here to win the Super Bowl. Period," Kolb said Monday at a news conference.
He said winning was the biggest factor in his decision to sign with the Bills.
"For me it was just straight, 'Hey, how can I go win, how can I go be successful,'" he said.
The Bills however, have the longest active postseason drought in the NFL at 13 consecutive seasons. Buffalo finished 6-10 in 2012, its eighth straight losing season.
Kolb will compete for the starting position with Tarvaris Jackson, who re-signed with the team earlier this offseason after backing up Ryan Fitzpatrick for the Bills last season. Fitzpatrick was released by the Bills this offseason and later signed with the Tennessee Titans.
The Bills also might select a quarterback in this month's draft. The team hosted Geno Smith for a visit last week. Syracuse quarterback Ryan Nassib met with the Bills on Sunday for a private workout. Bills coach Doug Marrone coached Nassib with the Orange.
Marrone said Kolb's signing won't alter the Bills approach to the draft, but did also cite the importance of adding veteran experience to the position.
"I'm not going to lie," Marrone said. "I think it was very important for us to get a veteran on the roster for that competition. Very important."
"There's very limited opportunities in this league. I've been lucky enough to have a few of them, hopefully I have another one here," Kolb said. "I plan on taking 100 percent care of that and making sure I do my part to play at the highest level."
The team didn't announce terms of the deal, but league sources told ESPN NFL Insider Adam Schefter late last month when Kolb agreed to sign that the quarterback received a two-year contract worth a maximum of $13 million.
"We wanted to add some veteran experience to the quarterback position on our roster, and we think we've added a good one by signing Kevin. He's a player we had targeted since he became a free agent, and he should be a strong candidate in the competition for the starting quarterback position," Bills general manager Buddy Nix said in a statement.
Kolb was released by the Arizona Cardinals last month after the sides were unable to reach an agreement on a restructured contract.
Thanks to injuries and unsteady play, Kolb appeared in just six games with the Cardinals last season, throwing for 1,169 yards with eight touchdowns and three interceptions.
Kolb, 28, threw for 17 touchdowns and 11 interceptions in two seasons with Arizona after being acquired from the Philadelphia Eagles. He was a 2007 second-round pick of the Eagles.
He said Monday he knows he has "to stay healthy" and that the injuries he's suffered in the NFL are "frustrating," especially after playing 50 straight games in college with Houston.
"I know I can play at this level," Kolb said Monday, acknowledging that he's been able to do it "here and there throughout my career -- two or three games at a time."
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.