City boss Manuel Pellegrini confirmed on Saturday that Lampard - who signed for new MLS franchise New York City last month after 13 glittering years at Chelsea - had opted to join the Premier League champions ahead of the 2015 MLS season, which begins next March.
And City made the move official on Tuesday, with England veteran Lampard expressing his delight at getting the chance to carry on playing in England prior to his debut campaign stateside.
"Joining up with Manchester City is a fantastic opportunity for me to continue to train and play at the top level and make sure I am in top condition for New York City," the 36-year-old told City's official website.
"It has been an amazing few days for me since the unveiling in Brooklyn and everyone connected with both clubs has been fantastic to me.
"This is a new chapter of my career and I'm really excited about the experience.
"I met Manuel and some of the players in New York and I'm looking forward to getting into training and making a contribution for Manchester City ahead of my move over to New York."
Pellegrini, meanwhile, hailed Lampard - Chelsea's all-time leading goalscorer - as a top-class addition to his squad, and feels the short-term switch to the Etihad Stadium represents a good deal for all parties.
"Frank is a world-class midfielder and this is an opportunity which works perfectly for everyone - the player, Manchester City, and New York City," said the Chilean.
"I'm looking forward to working with him and integrating him into our squad.
"New York have made a fantastic signing by recruiting Frank and I'm really pleased that we'll be able to have him with us for the first half of our season and help him prepare for his new challenge."
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