Lampard's confirmation comes hot on the heels of Sarri's return to the Italian Serie A with Juventus.
After an impressive spell in his first managerial role with Derby County, the 41-year-old will be in the dugout for his former club.
Lampard after signing a three-year contract with the London-based club said;
“It has been a fantastic experience for me, and I feel privileged to have managed such a prestigious club.
“Most of all, I want to thank the fans who supported me and the team from the day I arrived in the City. I wish everyone the best of luck going forward.
“Everyone knows my love for this club and the history we have shared, however, my sole focus is on the job in hand and preparing for the season ahead.
“I am here to work hard, bring further success to the club and I cannot wait to get started.”
Lampard's appointment comes nine days after Derby County granted him permission to negotiate with Chelsea.
The former West Ham United player becomes the 10th full-time manager appointed by Roman Abramovich since he bought the club in 2003.
Lampard made 648 appearances for the Stamford Bridge outfit as he won 11 trophies and scored 211 goals making him the only midfielder to score more than 150 goals in the Premier League history.
Having spent just a season in the MLS with New York City, Lampard retired from football in 2017.
