On 2 September 2014, Šćepović signed a four-year deal with Celtic for £2.3 million, having turned down a move the day before. Eleven days later, he made his debut as a starter in a 2–1 victory against Aberdeen at Celtic Park.
On 23 October, he scored his first goal for the club against Astra Giurgiu in the UEFA Europa League, scoring a header from an Anthony Stokes free kick in a 2–1 home win. Three days later, he netted his second goal for the club and his first in the league, in a 2–0 victory over Kilmarnock. The other goal of that game was a free kick from John Guidetti, earned after Manuel Pascali was sent off for a professional foul on Šćepović.
On 15 March 2015, Šćepović was an unused substitute as Celtic won the Scottish League Cup with a 2–0 win over Dundee United in the final at Hampden Park, with Stokes and Leigh Griffiths starting and Guidetti as a substitute. On 24 May, he scored in each half as Celtic concluded their fourth consecutive league-winning season with a 5–0 home win over Inverness Caledonian Thistle.