The Ivory Coast striker scored an impressive 31 goals in the Eredivisie last campaign and has now finalised his move to the Liberty Stadium
The Ivorian signed for Michael Laudrup's men earlier this month in a club record £12 million deal, eclipsing the £5.55m paid for Pablo Hernandez last season.
Bony is one of a whole host of new recruits by the Swans with Jonjo Shelvey, Jordi Amat, Jose Canas and Alejandro Pozuelo also arriving in South Wales this summer.
An announcement on the Swansea official website said: "Swansea City are pleased to announce that club record signing Wilfried Bony has been granted a work permit.
On signing for Swansea, Bony admitted that playing in the Europa League was a major attraction with the club set to play the first leg of their third qualifying round on August 1, having been drawn against Malmo or Hibernian.