The American-born Italy international arrived at Turf Moor from La Liga side Espanyol for £2.6m in 2023 and went on to make 45 appearances, scoring three times.
Koleosho, 21, spent the second half of last season on loan with Paris FC, going on to score three goals and provide one assist in his 18 games.
Paris FC have now confirmed that the winger has returned to the club on a permanent basis for an undisclosed fee, signing a deal until 2031.
Marco Neppe, Sporting Director of Paris FC, said: “Thanks to his first stint at the club, Luca is a player we now know very well. We absolutely wanted to bring him back.
“Luca is young and possesses great qualities; his profile perfectly matches the team's needs.
“We are certain that he will be able to realize his full potential here and contribute to the future successes of Paris FC.”
He follows Jaidon Anthony, Maxime Esteve, Lesley Ugochukwu, Loum Tchaouna and Quilindschy Hartman in leaving Turf Moor this summer.