On 22 June 2015, Serie A champions Juventus announced that Mandžukić joined the club from Atlético Madrid on a four-year contract for a fee of €19 million payable in three installments, including a possible extra €2 million in performance-related add-ons.
On 8 August he scored the opening goal in the 69th minute for Juventus with a header against Lazio in the 2015 Supercoppa Italiana, a 2–0 win in Shanghai. On 23 August 2015, he made an official league debut for Juventus, starting and playing the full 90 minutes in a 1–0 loss to Udinese, in the first league game of the 2015–16 Serie A season.
On 21 September 2015, it was confirmed that Mandžukić would be out for three weeks following a thigh related injury the day before in a 2–0 win over Genoa. However, he returned early, scoring Juventus's first goal, and temporary equaliser, as the team came from behind to win 2–1 away against Manchester City, during their opening match of the Champions League group stage, on 15 September 2015. On 25 October 2015, Mandžukić scored the final goal in Juventus's 2–0 home win over Atalanta in the 49th minute; this was his first Serie A goal in his 6th league appearance with the club. He scored again two games later, helping Juventus to defeat Empoli 3–1. On 25 November 2015, Mandžukić scored the winning goal in a 1–0 home win over Manchester City in the second leg of the Champions League group stage, to secure the club a spot in the round of 16. Due to these significant goals, as well as another one in a 3–0 away win against Palermo on 29 November, he was voted Juventus player of the month for November 2015. On 27 January 2016, Mandžukić sustained a muscle injury during the first semi-final leg of the Coppa Italia against Inter Milan, putting him on the sidelines for four weeks. It was initially feared that he would miss the first round of 16 leg of the Champions League against his former club, Bayern Munich. However, he returned to action earlier than expected, starting in the match against Bayern on 23 February, and setting up Paulo Dybala's goal in a 2–2 home draw.
Mandžukić scored once in Croatia's successful UEFA Euro 2016 qualifying campaign, opening a 1–1 home draw with Italy in Split on 12 June 2015. The following 4 June, both he and Nikola Kalinić scored hat-tricks in a 10–0 warm-up win against San Marino in Rijeka ahead of the tournament; the result was a record victory for Croatia.