Ayew’s time at the Liberty Stadium has come to a close after 141 appearances over two spells.
Ayew scored 35 of his Swansea goals in the past two seasons after returning from a 2018-19 loan spell at Fenerbahce.
Routledge has made over 300 appearance since joining Swansea in August 2011.
The 36-year-old was ruled out of the Championship play-off final defeat to Brentford last weekend after suffering a knee injury in the semi-final win over Barnsley.
“The club has offered a new one-year deal to long-serving forward Wayne Routledge as he continues his recovery from knee surgery,” Swansea said on its website.
Wales defenders Kieron Freeman and Declan John and Scotland winger Barrie McKay will leave the club at the end of their contracts later this month.
Freeman made just one appearance after joining from Swindon in January, while John and McKay had respective loan spells at Bolton and Fleetwood during the 2020-21 season.
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