Bony, who is currently on international duty with the Ivory Coast at the Africa Cup of Nations, moves to the Etihad Stadium after penning a four-and-a-half-year deal following days of negotiations between the two clubs.
The striker - signed from Vitesse for a club-record £12 million in 2013 - will leave behind a sizeable void at Swansea, having netted 34 goals in 70 appearances for the Liberty Stadium outfit, but says he will look back at his time in south Wales with great affection.
"I'm going to really miss Swansea - the club and its people," he told the club's official website. "But it's a big challenge that I had to take; one I'm excited about.
"I'd like to thank everyone at Swansea - from my playing colleagues, the coaches, medical team and the kit staff through to the chairman, who has been great with me. There are too many people to mention.
"The fans are up there at the top, though, because they've also supported me from the very first day I arrived, even when things weren't going so well for me. They've kept singing my name at the Liberty which has meant so much to me.
"They would even sing the Wilfried Bony song when I walked down the street, which is unbelievable. We would have a good joke about it.
"I only have good things to say about life in Swansea and the people because they’ve always shown me warmth – on and off the pitch. I'm going to miss everyone.
"I still believe that Swansea was the right club for me to join when I left Holland for the Premier League. I have no regrets, although it's going to be strange coming back to the Liberty to play against Swansea.
"But now was the right time for me to gain more experience and challenge myself with Champions League football and to try and win trophies.
"I have spoken to the coach [Garry Monk] and he has wished me good luck for the future. I would also like to thank him, not just as the coach, but also when he was a player last season, because he has helped me a lot.
"I will also speak to Ash [Ashley Williams] later to thank him as captain and to pass on my gratitude to the rest of the squad.
"It's a good squad that will continue to do well this season. I have no doubts about that."
