The 24-year-old striker from Sporting Gijon had agreed a four-year deal with the Scottish champions following talks last week.
He also passed his Celtic medical on Friday but late on Sunday changed his mind and seemed intent on remaining in Spain at Getafe.
However, this move did not materialise, opening the door for the second time on his switch to Glasgow.
It has been reported that the Getafe deal floundered on financial terms.
Scepovic has been capped eight times by his country and will remain at Parkhead until the summer of 2018.
He becomes the club’s sixth summer signing, joining Craig Gordon, Jo Inge Berget, Aleksandar Tonev, Jason Denayer and Mubarak Wakaso in Glasgow.