That's the confident prediction of former Hoops star and manager Davie Hay.
The 31-year-old became Ronny Deila's first signing when he put pen to paper on a two-year deal. And Gordon has wasted no time in getting down to work after flying out to join his new team-mates at their Austrian training camp.
With Forster's future still unclear - Atletico Madrid are tipped to bid £8million to bring in the Englishman as a replacement for Thibaut Courtois - the acquisition of the man capped 40 times for Scotland could not be better timed.
But, even if Forster sees out the remaining two years of his contract, Hay believes he will face more competition than ever before for the starting position at Celtic.
The man who led the club to title success in 1986 said: "If Craig has recovered fully from the knee injury which threatened to end his career, he will be pushing Fraser big time for the position of No.1 keeper.
"Fraser has improved a lot in the past couple of years, as his England call-up proves.
"But you have to remember just how good Craig was before he suffered his misfortune.
"He was the most expensive keeper in Britain when Sunderland paid £9m for him.
"And, before he had problems with his arm then his knee, he was performing very well in the top flight in England.
"Craig was developing into one of the best keepers Scotland has ever produced."
Hay asked: "Can he get back to that level after two years out? That's what we will all have to wait and see. If he can, it will be one of the best stories football has produced for many, many years.
"Whatever happens, it has been a good move by the club.
"If Fraser is sold - and I don't consider Craig's signing means that's certain to happen - they will bring in a lot of money and have a
more-than-capable replacement already on board for no cost.
"If Fraser stays, the competition Craig will provide - and he has made it clear he is not content to simply get a contract and sit back on the sidelines - will help ensure the consistency of performance is maintained.
"Craig has been given a second chance, and he is the type of guy who will be determined to make the most of it."
Gordon has not just set his sights on winning the No.1 spot at Celtic - he also wants to regain his position as Scotland's first choice.
Hay does not consider that aim to be a case of looking too far ahead.
"Craig's stated ambition regarding Scotland convinces me he is confident he can get back to being the keeper he was at his peak," said the man who played in the '74 World Cup for Scotland.
"That attitude has got to be a good sign for all involved."