Hagi started his career playing for the youth teams of Farul Constanța in the 1970s, before being selected by the Romanian Football Federation to join the squad of Luceafărul București in 1980, where he remained for two years. In 1982, he returned to Constanța, but one year later, aged 18, he was prepared to make the step up to play for a top team. He was originally directed to Universitatea Craiova, but chose Sportul Studențesc of Bucharest instead.

Hagi made his debut for the Romania national team in 1983, against Norway, in Oslo, at the age of 18. He scored his first international goal against Northern Ireland in 1984. The following year, he was made captain for the first time, in a World Cup qualifier against the same opponent.

In late 1986, Hagi transferred to Steaua București as the team prepared for the European Super Cup final against Dynamo Kyiv. The original contract was for a one-game loan only, the final. However, after winning the trophy, in which Hagi scored the only goal of the match from a free kick, Steaua did not want to release him back to Sportul Studențesc and retained him. During his Steaua years (1987–1990), Hagi played 97 Liga I games, scoring 76 goals, and netted 98 goals in total in 107 appearances for the club across all competitions. With the club, he reached the European Cup semi-final in 1988, and the final in the following year, while Hagi finished as one of the competition’s top scorers in the former edition of the tournament. Hagi also won three consecutive league and Cup doubles with Steaua between 1987 and 1989. His strong performances had him linked with Arrigo Sacchi’s Milan, fellow Serie A club Juventus, and German side Bayern Munich, but Nicolae Ceaușescu’s communist government rejected any offer.

After impressing at the 1990 FIFA World Cup, Hagi was signed by Spanish club Real Madrid on 27 June that same year; the La Liga side paid $3.5 million to Steaua București in order to acquire him. Hagi played two seasons with Real Madrid, which were largely unsuccessful, scoring 20 goals in 84 games, and only winning the Supercopa de España; some of his most memorable performances for the club included a hat-trick in a 5–0 home win over Athletic Bilbao at the Santiago Bernabéu Stadium, on match-day 22 of the 1991–92 season, and a 40-yard lob against Osasuna during the same campaign. He was subsequently sold to Italian side Brescia for 8 billion lira in 1992.

After two years at Barça, Hagi signed for Turkish club Galatasaray in 1996, at the age of 31. He had been the subject of a competing transfer offer from São Paulo FC. Although in the twilight of his career, at Galatasaray, he was extremely successful, and became highly popular among the Turkish supporters, due to his excellent performances for the club. Hagi was an important member of the Galatasaray team that went on to win four consecutive league titles between 1996 and 2000. In 2000, at age 35, Hagi had one of the best seasons of his career, winning every possible major title with Galatasaray that season. Most significantly, Hagi captained the club to win the 1999–2000 UEFA Cup after defeating Arsenal on penalties in the final, following a 0–0 draw; during the match, Hagi was sent off in extra-time for punching Arsenal captain Tony Adams. Consequently, Galatasaray became the first Turkish club to win a UEFA club competition title. The team’s UEFA Cup triumph was immediately followed by the UEFA Super Cup title, with a historic 2–1 win against Hagi’s former club Real Madrid in extra-time. The mass hysteria caused by these wins in Istanbul raised Hagi’s popularity with the fans even further, and prompted former France international Luis Fernández to say, “Hagi is like wine, the older it gets, the better it is.”

His son Ianis Hagi, who is also a footballer, was born in Istanbul, Turkey, in 1998, when he was playing for Galatasaray SK. Ianis currently plays for Scottish club Rangers. His daughter, Kira Hagi (born 1996), has started an acting career.

When he retired in 2001, Hagi was one of the most popular players in both Turkey and Romania. Hagi drew praise from the Galatasaray supporters for his performances during his time with the club, who adopted the chant “I Love You Hagi” in his honour.

Hagi retired from professional football in 2001, at the age of 36; that year, he was given a send-off in a testimonial game on 24 April, called “Gala Hagi,” featuring a team of Romanian All-Stars against a team of international All-Stars. At the time of his retirement, his 124 caps for his country were a national record, which has since been surpassed by Dorinel Munteanu. He currently still holds the record of most goals scored for the Romanian national team, alongside Adrian Mutu, with 35.

In 2001, Hagi was named the manager of the Romania national team, replacing Ladislau Bölöni, who left the squad to coach Sporting Clube de Portugal. After failing to qualify the team for the World Cup, however, Hagi was sacked. His only notable achievement during the six months as Romania’s manager was the win in Budapest against Hungary.

In 2003, Hagi took over as coach of Turkish Süper Lig side Bursaspor, but left the club after a disappointing start to the season.

Hagi then became manager of Galatasaray in 2004, leading the team to the Turkish Cup in 2005 final with 5–1 as a score against fierce rivals Fenerbahçe. His contract, however, was not renewed since his team was not able to win 2004–05 Süper Lig title over Fenerbahçe during the centennial of the club.

After Frank Rijkaard was sacked as coach, Hagi signed a one and a half-year contract with Galatasaray on 21 October 2010. His official presentation was held on 22 October. His former teammate from Galatasaray Tugay Kerimoğlu assisted him in Istanbul, but he was sacked on 22 March 2011 after a series of poor results in the Süper Lig.

In September 2014, Hagi appointed himself manager of Viitorul Constanța, in addition to being the owner and chairman of the club. Successfully avoiding relegation in his first season, Viitorul went on to be the season’s wonder in the 2015–16 season, finishing the first half of the regular season on 3rd place, which led Hagi to being named Romania Coach of the Year. Eventually, Viitorul finished the regular season on 4th place, earning their first play-off qualification. Viitorul finished the play-off on 5th place, but qualified for the UEFA Europa League third qualifying round due to Dinamo București’s insolvency. In their first European match, Viitorul were defeated 0–5 by Gent at the Ghelamco Arena, and were eliminated after a 0–0 home draw.