The deal is for six years and $30 million, a source told ESPN's Mark Schlabach.
Taggart, who was hired at Oregon in December 2016, went 7-5 in his first season with the Ducks. He replaced Mark Helfrich in Eugene after spending four seasons at South Florida, where he went 24-25, including 18-7 in his final two seasons.
"We thank Willie for his efforts at Oregon, and we wish him and his family all the best in the future," Oregon athletic director Rob Mullens said in a statement.
Taggart, a Florida native, has a 47-50 career head-coaching record but is regarded as one of the top up-and-coming offensive minds in college football and has strong recruiting ties in the state of Florida.
The 41-year-old interviewed with FSU officials on Monday. Charlie Strong, who replaced Taggart at South Florida, also met with FSU officials on Sunday.
Oregon had reportedly offered Taggart a little more than $20 million over five years to stay, but he's on the move back to the Sunshine State.
Florida State has scheduled a Wednesday news conference to introduce him.
Taggart replaces Jimbo Fisher, who left FSU to take Texas A&M's head-coaching job. Taggart becomes only the third head coach at Florida State in the past 43 years. Bobby Bowden guided the FSU program for 34 years and Fisher for the past eight years.
The Ducks, meanwhile, have named Mario Cristobal their interim head coach and will begin a national search for a permanent replacement. Cristobal had been serving as the team's co-offensive coordinator, run-game coordinator and offensive line coach.
"I am grateful to Mario Cristobal for his willingness to step up and lead our program through our upcoming bowl game," Mullens said. "The University of Oregon is a high-caliber academic institution with one of the premier college football programs in the country, and we are confident that we will find another outstanding coach to lead our tremendous group of student-athletes into the future."