The Blues confirmed the move via Twitter:
Per Chelsea's official statement, Lampard said:
"I am immensely proud to be returning to Chelsea as head coach. 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, 41, succeeds Maurizio Sarri as Chelsea boss after the Italian joined Juventus last month following just a season in charge in west London.
The former midfielder has only a season of senior management experience having taken over Derby County in May 2018.
In 2018-19, he led the Rams to sixth place in the Championship, but they missed out on promotion to the Premier League after losing 2-1 to Aston Villa in the play-off final.
Despite Lampard's relative inexperience as a manager, he will likely welcomed by the Chelsea faithful given his huge success as a Blues player.
He spent 13 years at the club between 2001 and 2014, winning three Premier League titles, four FA Cups, the 2011-12 UEFA Champions League and 2012-13 UEFA Europa League.
The former England international also scored 211 goals in that time, more than any other player in the club's history.
Lampard will be hamstrung initially by the two-window transfer ban Chelsea have been handed by FIFA for breaching rules relating to the registration of players under 18.
He will have to draw on Chelsea's youth ranks to supplement the current first-team squad, and he is reportedly preparing to bring the two groups closer together:
Due to the transfer ban, and the well-earned goodwill towards him at Stamford Bridge, Lampard could be given more time to succeed as Chelsea manager than many of his predecessors have.
But he has a major challenge on his hands, especially given he is making the step up to Premier League and Champions League management so early in his coaching career.