The Hoops have agreed a fee - reported to be around £3million - with the striker's Spanish club, Sporting Gijon.
Scepovic's representatives are now locked in talks with Celtic over personal terms on a contract expected to be for four years.
The Serbian will become the first purchase by Ronny Deila, who believes he can bring the physical presence he wants at the point of his attack.
Unless there are any last-minute hitches, Scepovic is expected to be in contention to make his debut in Sunday's SPFL Premiership game at Dens Park.
As Scepovic comes in, reports in Portugal claim Amido Balde is on his way back on loan to Vitoria Guimaraes.
Celtic also hope to finally complete the paperwork to bring Wakaso Mubarak in on loan from Rubin Kazan in time to be registered before the September 1 deadline for the group stage of the Champions League or Europa League.