City manager Manuel Pellegrini confirmed the deal Saturday after the club's International Challenge Cup defeat on penalties against Olympiakos at the University of Minnesota.
"From next week, on Wednesday, he'll start working with our team," Pellegrini said. "At the moment, he will start working with our squad because he is a member of the squad. He will be in the fight for a position. We have a very good team. He is one player more. We have a lot of competition, especially in the Champions League, so he is very important to our team."
Lampard signed a two-year contact with the New York club - owned by Manchester City and the New York Yankees - last month. The MLS team is scheduled to begin play next year.
The 36-year-old Lampard is Chelsea's all-time top scorer.
Pellegrini was asked about Lampard playing against his former club - with City scheduled to host Chelsea on Sept. 21 in the Premier League.
"I will talk about those things with him," Pellegrini said.