The Ivory Coast international, signed from Vitesse Arnhem earlier this month, is now expected to join the Swans for training on Thursday and could play in Saturday's friendly at Reading.
The 24-year-old had continued training with Vitesse while he awaited clearance to complete his move.
He can now be registered in time for the club's first Europa League qualifier against Malmo or Hibernian on August 1.
"Swansea City are pleased to announce that club record signing Wilfried Bony has today been granted a work permit," an announcement on the club's website read.
Bony was the top scorer in the Eredivisie last season after netting 31 goals in 30 games for Vitesse.