The club fast-forwarded by a day the signing which was earlier reported by Greennews.ng this morning.
The Sun UK reports that the Italy boss will move to Stamford Bridge after Euro 2016 to begin a three-year contract after Guus Hiddink leaves.
The club has also announced the deal on its official Twitter handle.
The 46-year-old said: “I am very excited about the prospect of working at Chelsea football club. I am proud to be the coach of the national team of my country and only a role as attractive as manager of Chelsea could follow that.
“I am looking forward to meeting everyone at the club and the day-to-day challenge of competing in the Premier League.
“Chelsea and English football are watched wherever you go, the fans are passionate and my ambition is to have more success to follow the victories I enjoyed in Italy.
“I am happy we have made the announcement now so everything is clear and we can end the speculation. I will continue to focus on my job with the Italian national team and will reserve speaking about Chelsea again until after the Euros,” it quoted the Italian tactician as saying.
Marina Granovskaia, the Chelsea director believed to be owner Roman Abramovich’s eyes and ears at the club, said: “We are very pleased to have recruited one of the most highly regarded managers in world football and we are equally pleased to do so before the end of the current season. This aids our future planning.
“I would also like to take this opportunity to thank Guus Hiddink, who has done a great job since he joined us in December.”