The 32-year-old, linked with a move across town to Arsenal, posted a farewell letter to the club's fans on Twitter.
Defeat would have left Arsenal nine points behind Liverpool, who also have a game in hand, but the way they reacted to going behind suggests they can still be a factor in the title race.
"Chelsea Football Club and Antonio Conte have parted company," the London outfit said on their website.
Chelsea slipped up in their push for a Champions League spot when they lost 1-0 at home to Arsenal in the Premier League on Wednesday with Emile Smith Rowe's first-half goal settling the London derby after a defensive mix-up by the hosts.
Jorginho's first-half penalty earned Chelsea a 1-0 victory over Tottenham Hotspur in the Premier League on Thursday.
Twelve months ago Liverpool were ripping up the record books on the way to their first English top-flight title for 30 years but defeat by Everton on Saturday left them mulling a host of far less flattering statistics.
Images from Monday's action in the Premier League.
Chelsea are banking on a lavish shopping spree to give them more bite up front and much-needed solidity in defence after coach Frank Lampard spent last season relying heavily on a crop of inexperienced home-grown players.
Champions Manchester City could only muster a 2-2 Premier League draw with Brighton & Hove Albion on Saturday.
Chelsea beat Manchester City 1-0 on Saturday to book a place in next month's FA Cup final, thanks to a second-half goal by Hakim Ziyech which ended City manager Pep Guardiola's dream of steering his side to an unprecedented quadruple of titles.
Chelsea paid a heavy price for a 3-2 defeat at West Ham United as first Liverpool, then Manchester City, leapfrogged them in the English Premier League title race on Saturday, with City ending the day on top for the first time this season.
Chelsea remain in fourth place, and are two points off third-placed Leicester City who have a game in hand.
A summary of Saturday's action in the Premier League.
Images from Saturday's action in the Premier League.
There has been no official confirmation of the agreement from either club but Sarri, who won the Europa League with Chelsea, is expected to sign a three-year contract, Sky reported.
Images from the English Premier League matches played on Saturday
IMAGES from the Champions League matches played on Wednesday
Postecoglou moves a step closer to making good on his reputation for securing silverware in his second season at clubs and delivering a first cup for Spurs since they won the League Cup in 2008.
West Ham United and Chelsea both narrowly avoided ignominious FA Cup exits with narrow wins against lower-league opposition but Everton marked Frank Lampard's first game in charge by sauntering past Brentford into the fifth round on Saturday.
Daniel Ceballos fired Arsenal into the FA Cup semi-finals with a stoppage-time goal that sealed a 2-1 win over Sheffield United
UEFA announces UCL final hosts for next four seasons.
Premier League champions Manchester City were drawn on Thursday with Juventus, Wydad AC and Al Ain in Group G for next year's FIFA Club World Cup in the United States.
IMAGES from the English Premier League matches played on Saturday.
Brighton & Hove Albion scored three times in the second half to fight back from two goals down and beat Manchester City
Timo Werner scored his first goal of the season as a much-changed Chelsea side crept into the fourth round of the League Cup by beating Aston Villa 4-3 on penalties after the Stamford Bridge clash ended 1-1 on Wednesday.
Headed goals from Anthony Martial and captain Harry Maguire earned Manchester United a hard-fought 2-0 win at toothless Chelsea on Monday amid more VAR controversy, putting them back in the hunt for a top-four Premier League finish. The VAR system made the headlines once again after two Chelsea efforts were ruled out and England international Maguire escaped sanction for a kick out at Michy Batshuayi.
Chelsea manager Frank Lampard believes his side are a long way short of the levels of Premier League Champions Liverpool and Manchester City, who have set the benchmark in terms of consistency. Lampard's Chelsea, currently third in the league, visit title winners Liverpool on Wednesday, chasing the three points they need to secure Champions League football next season.
Chelsea have made the first major transfer move ahead of next season after reaching an agreement with Germany's highly-rated RB Leipzig striker Timo Werner. The Premier League club announced on Thursday that they had struck an agreement with Leipzig on a transfer fee and on personal terms with the player, who had been strongly linked with a move to European champions Liverpool.
Chelsea have already opened the hotel on their Stamford Bridge stadium site to National Health Service staff in London, while the men's squad have donated money to the Chelsea Foundation to help support those in need during the crisis.
West Bromwich Albion secured a stunning 5-2 win over 10-man Chelsea at Stamford Bridge
The 28-year-old's move from Serie A to the Champions League holders is expected to be 97.5 million pounds ($135.26 million).
Chelsea extended their impressive turnaround under new coach Thomas Tuchel with a 2-0 home win over in-form Everton on Monday as Kai Havertz played a key role in both goals on his return to the starting 11.
Images from the English Premier League matches played on Saturday.
Guardiola said the expanded Club World Cup would make it even more difficult for clubs to manage player workload.
Images from the UEFA Champions League matches played on Wednesday.
Images from Wednesday's action in the Champions League.
Chelsea striker Tammy Abraham scored a late opportunist double to secure a 3-0 home win for Chelsea over West Ham United in the English Premier League on Monday.
A video circulating on social media that showed members of the Argentina national team singing about France striker Kylian Mbappe's African descent.
Several Chelsea players have not returned for pre-season training after testing positive for COVID-19, according to reports in British media.
Liverpool's Mohamed Salah ended his Premier League goal drought in style by scoring twice as the champions raided the capital again to crush West Ham United 3-1 on Sunday.
