A formal announcement will come Monday, the source said.
Weis, hired at Notre Dame five years ago when Urban Meyer turned the Irish down to come to Gainesville, is currently the offensive coordinator for the Kansas City Chiefs. Kansas City leads the NFL in rushing and ranks ninth in total offense.
The Chiefs are headed to the playoffs, and Weis will remain with them throughout the postseason. Weis won't go on the road recruiting at least for a week, but he will be to call recruits.
Weis won three Super Bowl rings in New England and then spent five years at Notre Dame. He started fast with the Irish, winning 19 games in his first two seasons, but he was fired after the 2009 season with a a 35-27 record in South Bend, Ind.
His strengths have been calling plays and recruiting, two things he'll be asked to do with the Gators.
He replaces Steve Addazio, who was under fire most of this season and got the blame for an offense that sputtered in just about every game. Addazio coached his final game Saturday in the Outback Bowl. He took the head coaching job at Temple last week.
New Florida coach Will Muschamp, whose roots are on the defensive side of the ball, said he wanted an offensive coordinator with college and NFL experience. Muschamp planned to scrap the spread-option offense in favor of a pro-style system.
Weis fits the bill perfectly, having tutored Tom Brady and Matt Cassel with the Patriots and Brady Quinn and Jimmy Clausen at Notre Dame. Now, he gets to work with John Brantley and maybe the top quarterback prospect in the country, Florida commitment Jeff Driskel.
The only concern with Weis might be health issues, something the Gators know all too well after coach Urban Meyer's recent scares.
Weis had a bad knee that left him barely able to walk during training camp and then had an acute gall bladder infection that required surgery.
He has battled weight problems most of his life. He underwent gastric bypass surgery in 2002 and lost around 90 pounds. But he lapsed into a coma after the operation and sued for malpractice, eventually losing. His knee problem probably traces to an accident in 2008 when one of his Notre Dame players ran into him during a game and tore his anterior cruciate ligament and medial collateral ligament.
The Associated Press contributed to this report.