The Australian international striker was signed from Croatia Zagreb for pounds 3m seven weeks ago, but quit the club within days of his arrival. Complaining of stress-related problems, Viduka left Scotland and set in motion a long- running dispute with the Parkhead club.
"Marko has informed Celtic he is fit, well, and committed to being a Celtic player for the next four years," Fergus McCann, the club's managing director, said. "The contractual position is detailed. However, we will act to ensure every party receives what they are due from the deal."
Viduka said: "I feel I have made a complete recovery. I simply want to concentrate on playing football and therefore do not want to discuss my contract or the transfer fee."
From the outset, Celtic's head coach, Jozef Venglos, refused point blank to discuss Viduka's situation and he offered few words in support of the player's return.
"I am pleased to have Marko back," he said. "He will add strength and versatility to our attacking options."
David Hannah, is ready to pitch in to what he believes will be a battle royal today as Celtic seek to avoid double knock-out disappointment against Airdrie.
They have already succumbed to the First Division side once this season, losing to a single-goal at the Shyberry Excelsior stadium in their defence of the League Cup.
Hannah missed out on that miserable Lanarkshire night as he has done on numerous occasions in a prolonged struggle to win a regular place.
But he believes his combative style could prove invaluable as Celtic look to mount a serious Scottish Cup campaign on the resumption of action north of the border after the winter shutdown. "I think the game will suit my style because Airdrie are going to be very physical in the middle of the park," he said.
The Cup holders, Hearts, are involved in the only all-Premier League meeting, at Motherwell tomorrow, with defender David Weir admitting: "Not much has gone right in the League. This is a massive game for the club. It is imperative that we win it."Reuse content