The Ivory Coast international's arrival from Swansea CIty was confirmed while the player was at the Africa Cup of Nations - a tournament his country eventually won on penalties against Ghana.
Yaya Toure was also part of that trophy-winning side, and City have struggled for form without the pair.
Manuel Pellegrini's men picked up their first win in five fixtures since New Year's Day with a 4-1 win at Stoke City last Wednesday and will welcome the return of two of their star players.
The club posted a vine on their official Twitter account of Bony - the Premier League's top scorer for the calendar year in 2014 - walking out for his first training session.
City face Newcastle United in the Premier League on Saturday.
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