He is a former France Under 20's international and has also represented the France Beach Soccer team. For the 2013–14 Ligue 2 season, Delort was named in the Team of the Year and nominated for Player of the Year.
Born in Sète, Delort started his career at FC Sète 34. He joined AC Ajaccio in 2008, having finished top scorer at France U19 league level with 30 goals. After coming through Ajaccio's youth ranks, he attracted interest from Bordeaux and Borussia Dortmund. After enjoying a trial at Borussia Dortmund, playing in the reserve team with Mario Götze and Shinji Kagawa, Dortmund offered him a contract. However, he chose to join Nîmes Olympique because of manager Jean-Michel Cavalli, claiming "a player who leapfrogs, burns his wings". Delort also turned down a contract offer from Bordeaux.
Delort played his first game of Ligue 2 for Nîmes on 30 August 2009, coming on as a 53rd-minute substitute against FC Metz. During the season, he was rarely used in the first team making only three substitute appearances.
Delort re-joined his original club AC Ajaccio on June 2010. He scored his first two goals at professional level on 15 September 2010 against Le Havre in the French League Cup before achieving his first goals in the French Cup on 12 November 2010. His first Ligue 2 goals contributed to victories against SCO Angers on 17 December 2010 and against FC Istres. He signed his first professional contract for three and a half years with AC Ajaccio on 28 January 2011. On 11 March 2011 he was one of the players involved in a mass brawl when he was replaced in the match against FC Nantes. As a result of the incident several players were given suspensions; both Delort and his teammate Carl Medjani received four-match bans. He earned promotion to Ligue 1 with AC Ajaccio during the 2010–11 season after finishing 2nd in the league.
On 31 January 2012, Delort signed a six-month loan deal with Ligue 2 club Metz where he scored 1 goal in 13 appearances.
He returned to AC Ajaccio for the 2012–13 season and scored his first goal in Ligue 1 on 27 April 2013 in a 2–1 win over Montpellier HSC. In that season he made 16 appearances in Ligue 1. In the same season, he scored 12 goals in 16 appearances for the club's reserve team.
In the summer of 2013, Delort joined Ligue 2 side Tours. He finished the 2013–14 season as joint top scorer in Ligue 2 scoring 24 goals in 36 matches and was named in the Ligue 2 Team of the Year as well as receiving a nomination for the Ligue 2 Player of the Year, eventually finishing runner-up to FC Metz’s Diafra Sakho for the award.
On deadline day of the summer 2014 transfer window, Delort signed for Championship side Wigan Athletic for a fee reported to be under £3 million. He was given the Number 49 shirt. Delort struggled at Wigan and amassed only 11 league appearances for the club, failing to score in any of them. In an interview with Hat Trick, he admitted that he had struggled to settle at Wigan following his sudden upheaval from France.
Having not been able to settle well in England, Delort re-joined Tours on loan until the end of the season on transfer deadline day in summer 2015. In doing so, he opted to take a 50% pay cut in order to obtain regular playing time again.
Delort completed a transfer to Stade Malherbe Caen on 2 July 2015. In his debut with Caen, Delort scored his first goal in a 1–0 defeat of Marseille on 8 August 2015. At the start of the following season, Delort refused to attend training during a protracted transfer saga with Liga MX side Tigres UANL.
On 2 September 2016, Delort's transfer to Tigres was officially announced becoming the second French player to join the team after André-Pierre Gignac. He signed a four-year contract while the transfer fee paid to Caen was reported as €8 million. On 22 October 2016, he scored his first goal in Liga MX with Tigres, against Pumas UNAM at the Estadio Olimpico Universitario in a 3-1 victory. He spent less than six months at the club, however, scoring 3 goals in 14 appearances, before returning to France to join Toulouse.
On 26 January 2017, Delort returned to France, joining Toulouse on a reported four-year contract and for a reported transfer fee of €6 million. He scored on his debut for the club on 2 February, netting the opening goal in a 4–0 win over Angers, and repeated the feat in his next two appearances against FC Lorient and SC Bastia.
Andy Delort played in the France Beach Soccer team managed by Eric Cantona in 2009. He was spotted by Laurent Castro during an amateur tournament in Sète who asked him to play in the qualification for the 2009 World Cup. He scored five goals in the qualifiers.
In 2011, he was selected by France Under 20's team by Francis Smerecki to play against the United States on 17 May 2011. He was then called to participate in the 2011 Toulon Tournament in June with the France team, but had to pull out of the squad having suffered an injury in a league game.
Liga MX: Apertura 2016
IndividualLigue 2 top goalscorer: 2013–14; 24 goals
UNFP Ligue 2 Team of the Year: 2013–2014
Player of the Month of Ligue 2: March 2014