Lampard, 36, left Chelsea in June after 13 years at the club but will be back in the Premier League for six months before joining up with City's affiliate club New York for their inaugural season.
"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," Lampard, who trained with City for the first time on Wednesday, said.
"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 (City manager) Manuel Pellegrini 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."
The move was welcomed by New York City FC sporting director Claudio Reyna.
"This is the perfect opportunity for Frank. He is in great shape following the World Cup, and training and playing with our colleagues in Manchester will enable Frank to be fit and ready for our inaugural training camp," he said.
Lampard, who scored a record 211 goals in all competitions for Chelsea, will be available for City's opening game of the season against Newcastle United and could feature against FA Cup winners Arsenal in next week's season-opening Community Shield.