Premier League champions Chelsea confirmed that 24-year-old Barkley had signed a 5-1/2 year contract, having initially turned down a move to Stamford Bridge in the close season.
No fee was disclosed.
Lampard was 23 when he joined Chelsea from West Ham United in 2001 and went on to score 211 goals for the Blues in all competitions.
Liverpool-born Barkley made 179 appearances for the Merseyside club he joined as an 11-year-old, scoring only 27 times in all competitions.
Comparisons with former Everton prodigy Wayne Rooney greeted his Everton debut as an 18-year-old in 2011 but despite earning 22 England caps his career has stalled somewhat.
He said that a move to Chelsea offers a "fresh start" and a chance to add more elements to his all-round game, specifically in the goalscoring department.
"I'm overwhelmed, I'm looking forward to it and I'm really excited to get started," Barkley, who has not played this season because of a hamstring injury, told Chelsea's website.
"To be given a fresh start at a new club like Chelsea, it's unbelievable for me. I'm looking forward to continuing where I left off at the end of last season and hoping to improve and add more goals to my game."
Barkley's first challenge will be to regain full fitness before trying to establish a role in Antonio Conte's team, which already features world class midfielders such as Tiemoue Bakayoko, N'Golo Kante and Cesc Fabregas.
A strong ball carrier who can also play wide or behind the main striker, the powerfully built Barkley would offer Conte more attacking options.
"He's very young. I think he has a lot of space for improvement ... He's strong physically and has good technique," Conte said on Friday before the deal was announced, adding that expectations should be tempered given that Barkley has not played for seven months."
Chelsea's club director Marina Granovskaia said Barkley was a player the club had admired for a long time.
"He possesses outstanding technical and physical attributes, matched with good experience of the Premier League and a strong desire to succeed at the highest level," she said.
(Reporting by Martyn Herman; Editing by Ken Ferris and David Goodman)
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