Pease, 47, is coming over from Boise State, where he spent the past six seasons, five as the Broncos' receivers coach and 2010 as offensive coordinator.
He has 11 years of play-calling experience, beginning at his alma mater, Montana (1996-98), and then Northern Arizona (1999-2000), Kentucky (2001-02) and Baylor (2003-05).
"Coach (Will) Muschamp and I share a lot of the same philosophies so this was a perfect fit," Pease said in a statement Wednesday. "I want to be multiple in our offensive formations and have a balanced attack with tempo. I firmly believe in being fundamentally sound and red-zone efficient. I want to develop our players in a pro-style offense that can help them at the next level."
Pease agreed to a three-year deal worth a little more than $500,000, a person familiar with the search told The Associated Press on Tuesday.
"When you go out and you talk to numerous people, many very qualified for this job, he really is the right fit for us," Muschamp said.
Pease's task will be to improve a Florida offense that finished 105th nationally in total offense (328.7 yards per game); 73rd in rushing (143.0 yards a game); and 89th in passing (185.7 yards per game) in Weis' lone season in Gainesville.
Quarterback John Brantley completed 60 percent of his passes this past season for 2,044 yards, but he threw only 11 touchdown passes.
Under Pease, the Broncos averaged 44.2 points and 481.3 yards last season and won 12 games.
Pease watched the Gators practice in Jacksonville for the Gator Bowl, and then spent last weekend in Gainesville with his wife. He apparently liked it so much he canceled an interview with national champion Alabama, which is looking for an offensive coordinator to replace new Colorado State coach Jim McElwain.
Pease begins work Friday and will spend his first month recruiting.
"No question, you've got two young guys who need a lot of fundamental work as they continue to progress as players," Muschamp said. "It was critical to me to bring in a guy that that's his expertise. Really good coaches coach a lot of stuff. You coach linebackers, coach secondary. You can train anybody to coach a front. Good coaches can coach a lot of different places. He's done that. Again, it shows you his track record of relating to people and doing a great job conveying the message."
Pease most recently worked with Boise State's Kellen Moore, who became the first quarterback in the Football Bowl Subdivision to win 50 games. Pease's resume also includes record-setting receivers Tyler Shoemaker, Austin Pettis, Titus Young and Jeremy Childs.
More importantly, Pease has experience in the Southeastern Conference.
At Kentucky, Pease helped turn the Wildcats into one of the top scoring offenses in the country. After posting a 2-9 season in Pease's first year, Kentucky finished 7-5 in 2002, which matched its best record since 1984, and ranked 23rd nationally and led the SEC in scoring offense.
Muschamp said calling plays in the SEC is different from other leagues.
"I just think there are more people to account for," he said. "I've said this before: the SEC is different because of the defensive lines in this league. ... Everybody's got good front people. Everybody's got people you've got to account for, and you've got to understand it's about mismatches.
"He's been through that. When you've got to line up against some of the defenses in this league and figure out how you're going to block those guys. You're not seeing it in one or two teams in your league. You're seeing it top to bottom, week in and week out."
Michael DiRocco covers University of Florida sports for GatorNation. He can be reached at firstname.lastname@example.org or on Twitter @ESPNdirocco. Information from The Associated Press was used in this report.