The deal will pay Kragthorpe $1.1 million a year, according to an official, who spoke to The Associated Press on condition of anonymity because the deal has not been completed.
Kragthorpe, who met with Louisville athletic director Tom Jurich on Tuesday in Tulsa, is expected to be introduced in Louisville on Tuesday afternoon.
The Louisville Athletic Association's board of directors was scheduled to meet at 4 p.m. ET and was expected to approve the hire.
Kragthorpe is 29-22 in four years at Tulsa after taking over a program that had lost 21 of its previous 22 games. The Golden Hurricane have been to three bowl games in Kragthorpe's four years.
Louisville, which won the Big East and beat Wake Forest decisively in the Orange Bowl, acted quickly to replace Bobby Petrino, who left to coach the NFL's Atlanta Falcons.
The football program is hosting prep players this weekend at a previously-planned recruiting event, and apparently already lost one prized recruit when quarterback Matt Simms -- the brother of NFL quarterback Chris Simms and son of NFL great Phil Simms -- reportedly said Monday he was withdrawing his oral commitment to Louisville.
While Cardinals running back Michael Bush announced he was entering the NFL draft on Tuesday, it remained to be seen if quarterback Brian Brohm could be persuaded to stay. Brohm, projected as a first-round draft pick by some experts, was expected to meet with Kragthorpe before deciding whether to return for his senior season or enter the draft.
Jurich and Kragthorpe have roots at Northern Arizona together. Jurich was the athletic director there in the late 1980s and early '90s, and Kragthorpe was NAU's quarterbacks coach from 1990-94.
Like Petrino, Kragthorpe has a track record as a strong quarterbacks coach and offensive tactician. He came to Tulsa after two years as the quarterbacks coach of the Buffalo Bills, and his Golden Hurricane teams have been prolific offensively.
Pat Forde is a senior writer for ESPN.com. The Associated Press contributed to this report.