Bony has signed a four-year deal at the Liberty Stadium following a successful medical at Swansea’s pre-season training camp in Holland earlier this week.
“This move has been talked about for quite some time, so I am delighted it is all completed,’’ Bony said.
“Now it is important that I focus my mind on the challenge ahead because I hope to make the Swansea fans very happy.’’
Bony finished as the Eredivisie’s top scorer last season with 31 goals in 30 games and won the Dutch player of the year award.
A picture of Bony posing with a Swans shirt alongside the Welsh outfit's chairman Huw Jenkins had appeared on Twitter on Tuesday evening, leading to speculation that the transfer would be announced.
The Swans are also in talks with QPR over a move for former Real Madrid star Esteban Granero, according to the player's agent.
The playmaker arrived at Loftus Road from Madrid in 2012 with the cash-rich Hoops looking to build a successful side in the Premier League.
However that has since turned sour, with the Rs relegated and keen to offload their top earners.
"The two clubs are talking about a transfer, it's true," Carlo Cutropia told Tuttomercatoweb.
"Michael Laudrup knows him very well from their time at Getafe, where together they had a great UEFA Cup campaign.
"Swansea are also looking at many Spanish players and play in Europe next year, [so] the destination would be absolutely acceptable to Esteban."
Granero, 26, made 27 appearances last season.
- Sports & Recreation
- Esteban Granero