Bony is away on international duty with Ivory Coast as they prepare for the Africa Cup of Nations and they looked to have broken the news of the transfer on Wednesday morning.
Both City and Swansea were keen to emphasise that was not the case, insisting the final stages of the deal had to be finalised.
All loose ends have now been tied up though and Bony will make the move to the Etihad Stadium once he returns from Equatorial Guinea.
???It???s a great feeling for me, it???s a big honour to be here and it???s a great challenge,” Bony told the Manchester City website.
???As a player it???s always good to be part of one of the biggest clubs in the world and it???s a good opportunity for me to be in that situation now ??? I???m really proud.
???I felt excited to wait for this moment and now it???s come, it???s fantastic.
???I think it???s a great decision for me – Manchester City is in the Champions League.?? You remember at the end of last season I said that if I want to move it will be to a team in the competition because it???s a great tournament that I really want to play in and one that I want to win.
???It???s a motivation for me to give my maximum to be in that place. City is a big club with great players with a lot of experience; I believe we can do it.???