Although the club have not yet officially announced the deal, manager Manuel Pellegrini confirmed on Saturday night that the England midfielder, who signed for City's sister club New York City FC this summer, will join up with the team on Wednesday.
"As you know Frank has signed a contract with New York City and will start working here [the United States] in January as the season starts in March," Pellegrini said.
"From next Wednesday he will start working with our team and will play for us. He will work with the squad and be a member of the squad. He will fight for a position. We have a lot of players in his position. He is one player more."