The 49-year-old returns to management having been sacked by the Blues at the end of the 2017-18 season, the Guardian reported.
“A new chapter in my life is beginning, I’m really excited,” said Conte on Inter’s official website.
“Through my work, I’ll try to repay all of the trust that the president and directors have placed in me.
“I have chosen Inter because of the club it is, because of the project’s sound basis and how ambitious it is. Because of Inter’s history. I was struck by the club’s transparency and the desire to bring Inter back to where it belongs.”
Conte spent two years at Stamford Bridge, winning the Premier League in his first season and the FA Cup in his final match in charge in May 2018. The Italian replaces the sacked Luciano Spalletti at the San Siro after the Nerazzurri finished fourth in Serie A this season, 21 points behind champion Juventus.
Ex-Italy boss Conte will be charged with closing the gap on his former side Juve, which he led to three league titles in three seasons as manager between 2011 and 2014.
“I’m sure that Antonio Conte is one of the best coaches out there,” said Inter president Steven Zhang.
“I’m certain that he’ll help us achieve our objective and fulfil our mission, one which has always remained the same: To make this club one of the best in the world again.”