The 24-year-old striker has been heavily linked with a move to the Swans with midfielder Leon Britton already admitting the transfer would be a massive "statement of intent" by the club.
That statement now appears to have been made with Bony having been pictured with a Swansea shirt and a deal taking the player to the Welsh club is expected to be finalised on Wednesday.
The transfer was also confirmed by Bony's agent Dalibor Lacina, who revealed that his client was looking forward to the chance to work with Michael Laudrup.
"We are glad that Bony has made the next step in his career after playing for Sparta Prague and Vitesse Arnhem," said Lacina, quoted in CTK.
"The transfer to the Premier League he has made his dream come true. Swansea is a big move for him and he is looking forward to working with the coach Michael Laudrup."
The fee is thought to be in the region of £12million and will help Laudrup build on last season's success with a European campaign to prepare for in 2013/14.
Bony was the top scorer in the Eredivisie last season having scored 31 goals in just 30 games for Vitesse.