The Ivory Coast international is believed to have been targeted by a number of Premier League outfits, but the Swans are thought to have won the race with an alleged £10m bid.
"The clubs are now talking to each other, Swansea has made Vitesse a bid and I hope it's good," Bony told Voetbal International. "Swansea is a wonderful club. It's my chance to play in the Premier League and they also play attractive football."
Chelsea and Newcastle United are thought to have also been keen on the striker.