Allan, 27, has agreed a three-year deal which will begin when his current contract at Celtic expires this summer.
This will represent the playmaker’s third spell at the club. He initially moved to Parkhead from Hibs in the summer of 2015 and returned on loan in the second half of last season.
Hibs have confirmed that the No.23 jersey worn by Allan in 2018 will be available for him again to wear next term.
Manager Neil Lennon told the club’s website: “It’s no secret that Scott is a player I admire and wanted back at Hibernian.
“He’s a player who suits the attacking brand of football we like to play. The type that gets supporters off their seats.
“We’re looking forward to having him back.”
Chief Executive Leeann Dempster added: “We’re delighted to have been able to come to a pre-contract agreement with Scott.
“It goes without saying that he’s a player our supporters hold in the highest regard and we were determined to bring him back to Easter Road.
“It’s an arena and a club that brings out the best in Scott and, from speaking to him, it’s clear that it means a lot to him.”