In the 2014 season, Deila's Strømsgodset were second in the league by the end of May after eleven games. The club had continued their impressive home record under Deila, having gone 44 league games unbeaten at their Marienlyst Stadium since June 2011; just one short of the all-time Norwegian record held by Rosenborg. However, Deila was beginning to attract foreign attention, and Strømsgodset had given him a new contract to run until 2016 in order to head off interest from Swedish champions Malmö who had unsuccessfully attempted to poach him in January. Despite this new contact, various media reports surfaced in the first week of June linking Deila to the vacant managerial post at Scottish champions Celtic.
Deila was appointed manager of Scottish Premiership club Celtic on 6 June 2014. He signed a 12-month rolling contract with the club, describing his appointment as a "magnificent honour" before stating his desire to deliver "attacking, exciting and entertaining football." Eleven days later, former Celtic and Scotland midfielder John Collins was appointed assistant manager. Deila described Collins as a "first-class coach" and stated that he "has ideas on football which are very similar to mine so I am sure he will be a great addition to my team."
After going unbeaten on a pre-season tour in Austria, Deila's first competitive match as manager of Celtic, a Champions League qualifying tie away against KR Reykjavik on 15 July 2014, ended in a 1–0 win for the Scottish club. The second leg of the tie ended in a 4–0 win for Celtic, securing a 5–0 aggregate win. The following qualifying round saw Celtic lose 6–1 on aggregate to Legia Warsaw. Despite this, Celtic were given a reprieve when it was discovered that Legia had fielded an ineligible player in the second leg. UEFA punished the Polish club by awarding the game 3–0 to Celtic, levelling the aggregate score at 4–4 and seeing the Scottish champions progress on away goals. Celtic went on to face Maribor in the next qualifying round. After an 1–1 draw away in the first leg, Celtic lost 1–0 in the return match at Celtic Park and went out on aggregate; dropping down to the Europa League.