The Ivory Coast international, who is currently on international duty for the African Cup of Nations tournament, will complete the deal within the next 48 hours.
The 26-year-old striker cost the Swans £12million from the Dutch club Vitesse Arnhem in July 2013.
Bony has scored nine Premier League goals so far this season and he was the highest goalscorer in the Premiership during the 2014 calendar year, scoring 20 goals.
Here’s how Bony compares to City’s current striker:
— Squawka Football (@Squawka) January 7, 2015