Leicester paid Celtic £9m to bring Brendan Rodgers and his backroom staff to the King Power Stadium, Sky Sports News understands.
The Foxes appointed Rodgers last month after sacking Claude Puel, who had gone seven matches without a win.
Rodgers had the opportunity to win an unprecedented Treble Treble with Celtic this season, but chose to return to the Premier League after Leicester made it clear they wanted to make an immediate appointment.
The former Liverpool boss is understood to have had a £6m release clause in his Celtic deal, which Leicester met.
The arrivals of assistant manager Chris Davies, first-team coach Kolo Toure and head of performance Glen Driscoll from Celtic are believed to have resulted in a £9m overall fee for Leicester.
Rodgers has won one and lost one of his first two games in charge at the King Power, while Celtic replaced the Northern Irishman with former boss Neil Lennon until the end of the season.