The Ghanian will move to the Premier League on a four-year deal after his contract at Marseille was not renewed.
Ayew will brought in to bolster the Swans’ attacking options this summer, the club having lost Wilfried Bony to Manchester City in January and his short-term replacement, loanee Nelson Oliveira, having returned to Benfica.
Ayew’s contract was allowed to run down at Marseille because of reported financial constraints at the club and he was linked with Tottenham and Roma.
The Ghanaian is the son of three-time African Football of the Year winner Abedi Ayew Pelle,??who spent five years at Marseille over two separate spells.
He began his senior career at Marseille, with stints on loan at FC Lorient and Arles-Avignon, before scoring over 44 league goals for the French Ligue 1 club.