The 46-year-old managed Empoli in the 2016/17 season but could not do enough to prevent the Italian minnows from succumbing to relegation from Serie A.
Former Napoli head coach Maurizio Sarri is the favourite to take over, with the club's top-flight opener a little over four weeks away.
Eden Hazard and Thibaut Courtois have both publicly said they were seeking clarity on Chelsea's summer plans before deciding whether to sign new long-term contracts, with the club facing a season without Champions League football after finishing fifth in the Premier League.
Conte spent two seasons in charge of the Premier League club, leading them to the title in his first year.
"We wish Antonio every success in his future career", the statement read.
Sex, Drugs, and a gay Imran Khan
She said that Imran was in a "live-in relationship" with his close friend Moby despite the former being married. Reham also writes that once she caught Imran red-handed snorting coke in the bathroom.
Conte's average of 2.14 points per game in the Premier League is bettered only by Alex Ferguson (2.16) and Guardiola (2.34).
But it will be another fresh start for Chelsea with Sarri becoming the club's seventh permanent manager since 2011.
His intense training methods angered senior players and he alienated the board with disparaging treatment of Spanish striker Diego Costa and constant carping over the club's failure to replace top players with those of similar ability. Conte's relationship with Chelsea's hierarchy was strained after disagreements over their transfer policy last season.
Chelsea seeks a 13th permanent manager under Abramovich's ownership, and at possibly the most turbulent period of the Russian billionaire's trophy-filled reign. Sarri and Higuain worked together at Napoli.
Russia World Cup star Aleksandr Golovin is another close to arriving from CSKA Moscow, along with Juventus defender Daniele Rugani.