The 25-year-old transfers from Championship outfit Aston Villa, as part of an exchange deal, which sees Villa's Neil Taylor move in the opposite direction.
In addition, the Jack Army will also pay an undisclosed fee for the frontman, who signed a three-and-a-half-year deal on Tuesday.
“I’m sure his brother [Andre Ayew, who played for Swansea between 2015 and 2016] has given him the inside track on the club,” Swansea head coach Paul Clement said, as reported by the club's official website.
“He is a very good acquisition. He’s versatile and dynamic to attack the lines and get in behind defences.
“He will certainly give us something different to what we’ve got.”
Ayew netted 10 times in 58 appearances for Villa, having been acquired from French club Lorient in 2015.
Seven of his 10 goals were in the Premier League in 2015-16, after which the club got relegated to the Championship.
This season, however, the forward has scored two goals in 21 league outings.
Lorient aside, Ayew has also played for Sochaux and Marseille in the French topflight.
He is currently on international duty with Ghana at the Africa Cup of Nations in Gabon, and expected to play an instrumental role when the Black Stars face Cameroon in the semi-finals on Thursday.