The former England midfielder, who racked up 626 appearances for Chelsea, left Stamford Bridge at the end of last season when his contract expired.
The 36-year-old will see out the season at champions City before completing his move sister club New York City in the summer.
Lampard was initially meant to join the MLS outfit in January, but he has no regrets about his spell at the Etihad.
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Frank Lampard delighted with his decision to join Manchester City
I'm very excited and I'm very fortunate
Frank Lampard
"I'm very excited and I'm very fortunate," the Blues legend said.
"This part of my career, coming to City, was something I never saw coming and when I look back and think, blimey, at 36 I got asked to come to the champions and a club with this pedigree of player here.
"I'm delighted that happened and I'm delighted with the future I've got and the opportunity to go on and play in New York and try to help there, but also be part of a new football club in one of the greatest cities in the world."
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