Driskel completed 10 of 16 passes for 114 yards and one touchdown against the Falcons while playing the bulk of the 27-14 win Saturday.
He beat out fellow sophomore Jacoby Brissett.
Driskel will make his first career start at quarterback when the No. 23 Gators (1-0) play at Texas A&M (0-0) on Saturday.
"(I) just feel like Jeff with his legs gives us some different variables in our offense that can help us as we move forward," Muschamp said. "It'll be Jeff's game to play. I told Jeff, 'I don't want you looking over your shoulder but you need to play well.'
"I have confidence in both guys. (We) can win with both guys. I just felt like at this time it's good to move forward with naming one guy and go with it."
Driskel, who played into the second quarter and the entire second half, was on the field for 52 of UF's 63 offensive snaps. Brissett got 11 and ended up completing 3 of 5 passes for 31 yards.
Despite that differential and Driskel's performance, Muschamp had said he wasn't sure who the starter would be for Saturday's game at Texas A&M. He wanted to speak to offensive coordinator Brent Pease on Sunday before making his decision.
"It's been a lifelong dream to be a quarterback at a university like this," Driskel said. "He just wants me to go out there and play and not worry about looking over my shoulder. He wants me to play loose and calm, and that's what I'm going to do."
Muschamp said Brissett handled the decision professionally.
"Jacoby wasn't very happy, and I respect that," Muschamp said. "I wouldn't want them to be pleased with it."
Driskel and Brissett had been competing for the starting job since spring practice, and Muschamp maintained throughout August practices that the two were even.
Both players actually started against Bowling Green, Brissett at quarterback and Driskel at receiver, because Muschamp said both deserved a chance to start.
Driskel was the backup to starter John Brantley through the first five games of the 2011 season, but he got hurt when forced into action against Alabama because of an injury to Brantley's ankle. Brissett overtook him and started the LSU and Auburn games, although Driskel played the second half against Auburn.
Neither player was particularly impressive in 2011. Driskel completed 47.1 percent of his passes for 148 yards and two interceptions. Brissett completed 46.2 percent of his passes for 206 yards and two touchdowns with four interceptions.
"Running the ball is a big part of my game," Driskel said. "I can make a play at any time. Any time the pocket breaks down or something happens, I feel like I can get outside."
Florida has been searching for a big-time quarterback since former Heisman Trophy winner Tim Tebow left Gainesville following the 2009 season.
Brantley struggled in two seasons as the starter, and it remains to be seen whether Driskel will do better.
Muschamp believes his experience from last year should help.
"That position's difficult to play at any stage of your development," Muschamp said. "But it's really difficult to play as a freshman quarterback in the SEC. I think both of those guys were put in very difficult situations last year. I think it was great experience for them now. It was very trying on me, but for them it was a very beneficial experience. Again, I think that both guys, and that's why I felt like we needed to make a decision on one, they need snaps. They need game-time snaps.
"There's going to be still a growing curve here. It's not all going to be perfect. I understand that. It's part of the growing process at that position."
Information from The Associated Press was used in this report.