The 25-year-old Serbia international, signed from Sporting Gijon on deadline day last August, failed to find a regular start at the club, making only one substitute appearance this season.
Scepovic has made 26 appearances for the club, scoring six goals and found himself behind Leigh Griffiths and summer signing Nadir Ciftci in the pecking order at Celtic Park.
Celtic announced his exit in a short statement, in which the club said: “Everyone at Celtic sends Stefan their best wishes, and hope that he and Getafe have a successful season.”
The Scottish champions are closing in on Inverness midfielder Ryan Christie and Croatian centre-back Jozo Simunovic from Dinamo Zagreb.
Caley Thistle have given Scotland Under-21 international Christie permission to speak to the Parkhead club who have agreed a fee for Simunovic, with discussions continuing.
Simunovic, 21, has eight caps for the Croatia Under-21 side and could be regarded as a replacement for Dutch defender Virgil van Dijk, who has been heavily linked with Southampton with the fee reported to be as high as £11million.
Elsewhere, there could be one or two new signings at Motherwell before the deadline passes.
Robbie Muirhead joined Partick Thistle from Dundee United on loan until January 4.
The 19-year-old forward was recruited from Kilmarnock by United on deadline day in the winter transfer window and scored two goals in 15 appearances.
A statement on Thistle’s official website confirmed the deal and said: “All at Thistle welcome Robbie and wish him all the best during his loan spell at Firhill.”