Lampard, 41, has left Championship side Derby County to take over at a club where he spent 13 years as a player.
He succeeds Maurizio Sarri, who left Stamford Bridge in June to take charge of Italian champions Juventus.
Lampard led Derby to the Championship play-off final, where they lost to Aston Villa, in his first season as a manager.
The former England international made 648 Chelsea appearances, winning 11 major trophies with them.
He takes over with Chelsea under a transfer embargo after the club were given a two-window transfer ban by world governing body Fifa – a decision they are appealing against at the Court of Arbitration for Sport.
“I am immensely proud to be returning to Chelsea as head coach,” said Lampard.
“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.”
The appointment comes nine days after Derby gave Lampard permission to talk to Chelsea and 18 days after Sarri left Stamford Bridge.
Lampard is the 10th full-time manager appointed by Roman Abramovich since he bought the club in 2003.
Chelsea director Marina Granovskaia said Lampard’s Championship play-off final appearance with Derby demonstrated that he was “one of the most talented young coaches in the game”.
“It gives us great pleasure to welcome Frank back to Chelsea as head coach,” she said. “Frank possesses fantastic knowledge and understanding of the club.”
Derby assistant manager Jody Morris and first-team coach Chris Jones have also joined Lampard at Stamford Bridge, while former team-mate Petr Cech was appointed as technical advisor last month.
‘Super Frank’s’ Stamford Bridge connection
Lampard joined Chelsea from boyhood club West Ham for a fee of £11m in 2001.
He won a Champions League and a Europa League at the club, while also helping them to win three Premier League titles, four FA Cups and two League Cups.
Chelsea’s title win in 2004-05 was their first in half a century and Lampard scored 13 league goals that season, including both in a 2-0 victory at Bolton that sealed the top-flight crown.
He scored 10 or more Premier League goals in 10 successive seasons for Chelsea and is the club’s all-time record goalscorer with 211.
Lampard left Stamford Bridge in June 2014 and had a stint at Manchester City, where he scored six goals in 32 appearances.
He then joined New York City in Major League Soccer in the US, making his debut in August 2015, before ending his 21-year professional playing career in 2017.
Lampard won 106 England caps after making his international debut in 1999 and went on to score 29 goals for the Three Lions.
He appeared in three World Cups and one European Championships.
The former midfielder said he did not want to be a “clone” of any of the club’s previous managers despite “rising expectations” on and off the pitch.
“Expectations at Chelsea will always remain, because of what the club has done in the last 15 years and I like that, I enjoyed that as a player,” he said.
“I enjoyed my first year on this side of the fence and I am determined to keep on going.”
A new focus on youth?
Christian Pulisic, a £58m signing from Borussia Dortmund, has replaced talisman Eden Hazard but Lampard will be forced to work with limited resources in his first season after the club was put under a transfer embargo.
Chelsea have a plethora of players on loan at Premier League and Championship clubs, including Kurt Zouma at Everton and promotion-winning Tammy Abraham at Aston Villa, and many are expected to be recalled.
Lampard also worked closely with two Chelsea players at Derby, both Mason Mount and Fikayo Tomori featuring heavily in his spell at Pride Park.
“There’s a nice balance of the older and younger players,” said Lampard.
“I’m excited about the current crop of youngsters, especially seeing the work that has gone into the academy over the years.
“I’ve seen the players – I worked with Mason Mount last year and you can see their attitude, how they hold themselves and their manners.
“I want to dangle the carrot and ask them can you perform? Can you get in the team?”
The new manager will have to succeed where his predecessor failed in giving sufficient game time to Callum Hudson-Odoi and Ruben Loftus-Cheek, two of Chelsea’s most promising youngsters.
Midfielder Loftus-Cheek has recently agreed a new five-year deal at his boyhood club, but Lampard will have to convince Hudson-Odoi to remain in west London despite ongoing interest from German giants Bayern Munich.