The 24-year-old has signed a four-year contract with the Scottish champions despite having left Celtic in the lurch going into the final day of the transfer window.
Celtic are also trying to complete the loan signing of Manchester City striker John Guidetti tonight after letting forwards Teemu Pukki, Amido Balde and Holmbert Fridjonsson leave Parkhead on a temporary basis.
Guidetti joined City as a 16-year-old, briefly returning to Swedish side IF Brommapojkarna on loan, before making his debut for the English club in 2010.
He spent some time on loan at Burnley before hitting the heights at Feyenoord with 20 goals in 23 games during a sensational loan spell in 2011-12, the highlight of which was a hat-trick against Ajax.
He made his full international debut during that season but missed the chance to play in Euro 2012 when illness caused a leg problem that kept him out for a lengthy period.
Guidetti returned to action last season and joined Stoke on loan in January, making six appearances off the bench. Palermo, Ajax, Fiorentina and Olympiacos were all linked with a move for the player this summer, but Celtic appeared to be heading up the chase after opening talks earlier this evening.
Described as a hard-working player with an eye for goal, he was photographed apparently entering Celtic Park last night after a day in which Celtic tried frantically to make up for lost time in their mission to sign a new striker, while allowing three other forwards to leave on loan.
Pukki joined Brondby, as did young Icelandic striker Fridjonsson, while Balde moved to Dutch outfit Beveren.
The club had done everything bar secure the signature of Scepovic, of Sporting Gijon, on the prepared contract before he performed a U-turn last night. However, the 24-year-old's mooted move to Getafe failed to materialise and an extraordinary chain of events was complete when Celtic announced his signing on their official website shortly after 10pm.
Earlier, Celtic chief executive Peter Lawwell had said: "Last night we were told he didn't want to come, he had changed his mind, which was extremely disappointing.
"We spent a lot of time on it. We'd agreed with the club and himself. We were just at the point of signing the contract, he'd got his work permit, he'd gone to Paris on Friday to have an appointment with the embassy, which went well. The plan was he was going to go back and pick it up today.
"He passed his medical on Saturday. I spoke to him on his way back from his medical on Saturday afternoon and everything was fine.
"So we were bitterly disappointed and we don't understand it."
Lawwell reiterated that Dutch defender Virgil van Dijk would not be leaving.
"(Manager) Ronny (Deila) was clear yesterday and that's the situation," he said. "Virgil will be staying and that's a boost for the club."
Scotland Under-21 international Dylan McGeouch has moved from Celtic Park to Hibernian on loan until the end of the season.
Hibs, who failed in a bid to re-sign Leigh Griffiths on loan from the Hoops, have also brought in 19-year-old Southampton striker Jake Sinclair on a season-long loan.
Ross County have re-signed Dundee United forward Michael Gardyne on loan until January 19, despite sacking manager Derek Adams and director of football George Adams last week.
Meanwhile, Hearts have loaned striker Gary Oliver to Stenhousemuir until January 5, one week after he scored in a League Cup win against the Warriors.
Goalkeeper Lee Hollis has left Tynecastle following a short spell as emergency cover for the injured Neil Alexander and Scott Gallacher.