Ćorić was born in Zagreb to Herzegovian Croat parents from Široki Brijeg; his father, Miljenko, is a football manager in the Zagreb area with whom Ante attended training sessions starting at a very young age. He started playing football at the age of 5 at Hrvatski Dragovoljac. When he was 9 years old, he signed for the youth academy of NK Zagreb. In 2009, Ćorić joined the youth academy of Red Bull Salzburg, despite the interest from other clubs, including Bayern Munich, Chelsea, and Barcelona. On joining the club, Ćorić commented, "I wanted to become a Red Bull Salzburg player because my team-mates here are better than players of the same age anywhere else. We train better and more often than others. And I was very impressed by how warmly I was welcomed." In 2013, after four years in Salzburg, Ćorić returned to Croatia and signed with Dinamo Zagreb for a fee of €900,000.
Dinamo Zagreb
On 16 April 2014, Ćorić made his senior debut against RNK Split, coming in as a 69th-minute substitute for Ivo Pinto. On 26 April, he made his first start in a 1–1 draw against Lokomotiva Zagreb. On 10 May, he scored his first senior goal for Dinamo in a 1–2 loss to NK Istra 1961. On 18 September, Ćorić came on as a 77th-minute substitute and scored the fifth goal in Dinamo's 2014–15 Europa League opener against Astra Giurgiu, a 5–1 win. With this goal, he became the youngest goalscorer in Europa League history, at the age of 17 years and 157 days. In 2015, the newspaper, Večernji list, awarded Ćorić the Croatian Hope of the Year award. In his nearly five seasons at the club, Ćorić made 143 appearances, winning four league titles, and two cup titles, and was named by the Italian newspaper, Gazzetta Dello Sport, as one of the "30 Best U20 Players in Europe" in 2017.
Roma
On 28 May 2018, Ćorić joined Italian club A.S. Roma for a reported fee of €8 million and signed a five-year contract on €1 million salary per year, after passing his medical.
Ćorić played with Croatia's youth teams, from 2012 to 2016, and made his senior international debut in a 1–0 win over Moldova on 27 May 2016, entering as a half-time substitute. In May 2016, he was selected in Croatia's 23-man final squad for UEFA Euro 2016. Ćorić was not selected for the 2018 FIFA World Cup preliminary squad.
