Pukki signed a four-year deal with Celtic from FC Schalke 04 for an undisclosed fee on 31 August 2013. He scored on his debut in a 3–1 win against Hearts on 14 September 2013 and again on his home debut against St Johnstone on 21 September. On 26 January 2014 he scored against Hibernian. Overall though, Pukki’s first season at Celtic was considered something of a disappointment as he struggled with form and failed to fill the void left by Gary Hooper who had left at the start of the season. Pukki himself later acknowledged the lack of impact he had made, admitting he initially felt playing in Scotland would be “easier” than in Germany. He found the speed and physical nature of the game in Scotland difficult to adjust to, and stated “Scottish football is not easy. It’s not a bad league at all”.
On 8 July 2014, Pukki scored his first Celtic hat trick in a pre-season friendly against LASK Linz in a 5–2 victory for Celtic. Pukki scored twice in Celtic’s victory against KR Reykjavik at Murrayfield Stadium in Celtic’s UEFA Champions League qualifying match, the match ended 4–0 with Celtic winning 5–0 on aggregate. However, he struggled to make any impact in the next qualifying round matches against Legia Warsaw and was substituted at half-time in the league defeat to Inverness Caledonian Thistle on 6 August 2014.