The 24-year-old scored 31 goals in 30 league games for Dutch side Vitesse last season, and has now moved to the Liberty Stadium in a club record deal which eclipses the £5.55 million paid for Pablo Hernandez last season.
“This move has been talked about for quite some time, so I am delighted it is all completed," Bony told the club's official website.
|66/1||Swansea are 66/1 with Coral to win the Europa League
Goal reported on Wednesday that the striker was due to complete a move within 24 hours, having already completed a medical at the Swans' pre-season training camp in Holland, where he watched in full club kit as the Capital One Cup winners registered a 10-0 friendly win over Haaglandia.
The Ivory Coast international's goal-scoring exploits helped Vitesse to a fourth-place finish in last season's Eredivisie, meaning they could face Swansea in the Europa League's third qualifying round.
Bony admitted the prospect of European football played a big part in his decision to join Michael Laudrup's side, having previously finished as the Europa League's top goalscorer with nine goals for Sparta Prague back in 2010-11.
“The Europa League is my first focus," he added. “I enjoy playing in Europe; I am used to it."
“I am looking forward to joining the training camp out here in Holland as a Swansea player and building up good communications with the team and coaching staff as quickly as possible.’’
The Ivorian is Swansea's sixth major signing of an already busy summer, joining Jonjo Shelvey, Jordi Amat, Jose Canas and Alejandro Pozuelo in linking up with the Capital One Cup winners, while Jonathan de Guzman loan deal has also been made permanent.