The Ivory Coast star completed the transfer from Swansea to City for £28m (€36m), the joint seventh highest transfer between two British clubs.
The 26-year-old is on international duty with the Ivory Coast ahead of the African Nations Cup, which starts in Equatorial Guinea this weekend and could prevent his City debut until the middle of next month.
Bony has signed a four-and-a-half year contract at the Etihad Stadium and will wear the number 14 shirt. He joins the English champions after scoring 34 goals in 70 appearances for Swansea following his £12m move from Vitesse Arnhem in 2013.
“It’s a great feeling for me, it’s a big honour to be here and it’s a great challenge,” Bony said.
City manager Manuel Pellegrini said he was delighted to be adding the muscular Bony to a strike force which already includes Sergio Aguero, Edin Dzeko and Stevan Jovetic.
“He is difficult to mark because he is so strong,” Pellegrini said. “He is an intelligent footballer who has skill and power. His goals record has been excellent since he came to England. He adapted quickly to the game here and I think he will settle in at City quickly.”
Bony’s departure means Swansea have almost doubled their transfer record for selling a player, the previous highest fee being the £15m Liverpool paid for midfielder Joe Allen in 2012.
Meanwhile Jermain Defoe was yesterday undergoing a medical at Sunderland as he closes in on a return to English football. The 32-year-old Toronto FC striker is set to complete his switch to the Black Cats today.
Sunderland have been engaged in advanced talks with Defoe in recent days and now look to be closing in on a capture they hope will significantly boost their attacking threat.
The Black Cats have turned to the former Spurs front man after scoring just 18 goals in their opening 21 League games, with Steven Fletcher, Connor Wickham and Altidore having contributed only six. US international Jozy Altidore could move in the opposite direction as part of the deal.