Hagi was born in Istanbul, where his father Gheorghe was playing for Galatasaray. He joined the Gheorghe Hagi football academy at the age of 10, and made his Liga I debut on 5 December 2014 with Viitorul Constanța at the age of only 16, when he came on as a last-minute substitute for Silviu Pană in a 1–2 home defeat to FC Botoșani, his maiden appearance being handed by his father. On 29 May 2015, Hagi scored his first goal as a senior, contributing to a 4–4 draw against the same opponent while also acting as a starter for the first time. In June, he gained team captaincy. Hagi scored his second league goal against ACS Poli Timișoara, in a 4–0 home win on 21 August 2015, a few days after having missed a penalty against Concordia Chiajna. In October, he was named by The Guardian as one of the 50 best young footballers in the world born in 1998. On 10 July 2016, Hagi joined Fiorentina for a €2 million transfer fee. He made his league debut on 23 October, replacing Josip Iličić late into a 5–3 away triumph over Cagliari. In April 2017, Hagi was nominated for the European Golden Boy award.
Return to Viitorul Constanța
Hagi returned to Viitorul Constanța on 18 January 2018 for a reported €2 million, with Fiorentina being entitled to 30% of a future transfer fee. In July, he was again nominated for the European Golden Boy award. Hagi's second spell at his father's team was proven to be more fruitful, managing to score twenty goals in 53 matches all competitions comprised. He won his first career trophy on 25 May 2019, after Viitorul defeated Astra Giurgiu 2–1 in the Cupa României final.
Genk
On 12 July 2019, Belgian defending champions Genk announced the signing of Hagi on a five-year contract. Press reported the transfer fee at €8 million with performance bonuses included, although some sources gave out the sum as being €10 million for 85% of the players's economic rights plus bonuses. Viitorul executive president Gheorghe Popescu confirmed that the club also retained interest on the capital gain of a potential future transfer. On 26 July, in the Belgian First Division A opening fixture, Hagi made his debut by coming off the bench and scoring the winner in a 2–1 victory over Kortrijk. He recorded his next goals on 28 September against Sint-Truiden, netting both from the penalty spot but with different legs, and also assisted Théo Bongonda in the 3–3 draw. He played in five of Genk's group stage matches in the UEFA Champions League, as his side finished fourth behind Liverpool, Napoli and Red Bull Salzburg respectively.
Rangers
Hagi joined Scottish Premiership club Rangers on a six-month loan with an option to buy on 31 January 2020. One day later, he made his first appearance for the club as a substitute in a goalless draw with Aberdeen. On 5 February, Hagi started and scored the winner in a 2–1 success over Hibernian. On 20 February, Hagi scored a brace against Sporting Braga in the UEFA Europa League helping his side win 3-2. In late May 2020, Rangers announced they had signed Hagi permanently from Genk on a "long-term" contract.
Considered to be a promising young footballing talent, Hagi's playing style has drawn comparisons with that of his father's due to his dribbling skills, passing, two-footedness and playmaking ability. Although his preferred role is as an attacking midfielder, he is a quick, agile and versatile midfielder who is also capable of playing in several advanced roles, and has also been used as a winger, a second striker or even a central midfielder on occasion. Due to his vision, technique and eye for goal, he is both capable of creating chances for his teammates and scoring goals himself.
Personal life
Hagi has an older sister, Kira, who is an actress. He is sponsored by Nike apparel.
