Deila was surprisingly 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 a credible 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.
On 13 August, Ronny Deila won his opening Scottish Premiership game, beating St Johnstone 3–0, although the performance was less than convincing. Deila’s second league match, and his first game at Parkhead, saw Celtic defeat Dundee United 6–1 in a performance that BBC Sport described as being “full of drive, skill, belief and… goals.” Generally though, Celtic were unconvincing in the early stages of the league, but improved as the season progressed and also qualified from their Europa League group. These improved performances saw Deila win the Manager of the Month award for November 2014. By February 2015, Celtic had won 15 of their last 17 domestic games and comfortably defeated Rangers 2–0 in the semi-final of the Scottish League Cup. Celtic played Inter Milan in the last 32 stage of the Europa League, rallying to draw 3–3 at Parkhead from an early 0-2 deficit in a pulsating encounter, then losing 1–0 in Milan to go out on aggregate despite a highly credible performance. In the league, Celtic thrashed second placed Aberdeen 4–0 on 1 March to go six points clear with a game in hand and a vastly superior goal difference. It was Celtic’s eighth consecutive win in the league, and the turn around in form saw previous critics of Deila review their opinion of him. Former Celtic striker John Hartson had branded Deila as “clueless” in October, but stated four months later that Deila had “turned it round”, praising his Celtic side for playing “brilliant football.”
Deila won his first trophy at Celtic on 15 March; Celtic defeating Dundee United 2–0 in the League Cup Final. Kris Commons and James Forrest were Celtic’s goalscorers, whilst Stefan Johansen won the Man of the Match award.
Deila’s Celtic team won the Scottish Premiership on 2 May 2015, with three games to spare, following their rivals Aberdeen’s loss to Dundee United. Celtic finished the season in style, as Ronny’s Celtic side beat Inverness 5-0 on 24 May 2015.
In August 2015, Celtic failed to progress from the UEFA Champions League playoffs, having failed to overcome Malmo, and were consigned to playing in the Europa League that season. In November, Celtic exited the Europa league, having finished bottom of their group. On 17 April 2016 Celtic played their old rivals, Rangers, in a Scottish Cup semi-final at Hamden. The match went to extra time before Celtic lost the match on penalties. Three days after the defeat and following intense speculation, Deila announced that he would step down at the end of the season. Celtic clinched the Scottish Premiership title following a win over nearest challengers Aberdeen on Sunday 8 May.