The move was first discussed soon after Lampard was revealed as NYCFC's second Designated Player on July 24.
Manchester City manager Manuel Pellegrini confirmed the move on Saturday, and it was officially announced Wednesday.
“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 said in a statement.
“It's been an amazing few days for me since the unveiling last week, 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.”
NYCFC have loaned a number of their already-signed players out to foreign clubs as they prepare for their inaugural MLS season.
Designated Player forward David Villa will play the last half of 2014 with Australia's Melbourne City FC, while defender Jeb Brovsky and midfielder Andrew Jacobson are playing for teams in Norway.
Goalkeeper Josh Saunders is on loan at the NASL's San Antonio Scorpions.
