Marc-Antoine Fortune's agent Michael Manuello has confirmed that the Nancy striker will sign for Celtic at some point in the next few days.
The striker is set to reject the offer from Hull City and opt for a reunion with Hoops manager Tony Mowbray, who he worked under at West Brom last season.
The 28-year-old scored five goals in 17 league appearances while on loan at the Hawthorns from his French club, convincing Mowbray to bring him to Parkhead.
Manuello also highlighted that everything should be completed so that Fortune would be available to fly with the rest of the Celtic squad to Australia on Thursday to begin pre-season training.
"Marc has made his decision and he will be in Glasgow on Tuesday," he told the Hull Daily Mail.
"He will look around the club and do some things which I do not need to be at. We still have some details to discuss with Celtic.
"It is nothing major but with every transfer you have to take care. There are some discussions to be finished but if things are normal he will sign for Celtic.
"I'll arrive on Tuesday night and I expect by Wednesday night everything will be OK for him to sign.
"We are aware that the squad is going to their training camp in Australia on Thursday."
Fortune, who is said to have cost the Old Firm club around £3.8million, is thought to have been swayed by the lure of UEFA Champions League football although Celtic will have to come through qualifying for this year's competition.