Allan, 27, has signed a three-year deal to begin in July although the speculation will now centre on whether Hibs manager Neil Lennon can persuade Celtic to part with the playmaker early. It is believed Hibs have been offered little encouragement on this front so far.
Lennon, meanwhile, is also understood to be keen to add a winger and a goalkeeper before the January window shuts. Hibs have lost wideman Martin Boyle to injury for the remainder of the season.
The Hibs boss told the club’s official 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.”
Allan started his career at Dundee United before earning a move to West Bromwich Albion. However a string of injuries hampered his time in England and he returned north in the summer of 2014 to join Hibs.
His impressive performances under Alan Stubbs alerted the attentions of Rangers and Celtic, and Allan opted to join the Parkhead side in a £275,000 deal.
But he has made just three first-team starts and come off the bench 14 times for Celtic and was farmed out to Rotherham and Dundee on loan before making a temporary move back to Easter Road last January.
Allan has turned out for Hibs on 57 occasions over his two previous spells at the club, netting six goals in total.
Lennon has already secured the services of Ryan Gauld on loan from Sporting Lisbon but is still keen to add more.