The Ghanaian completed a three-and-a-half-year move on transfer deadline day last month after struggling for opportunities at former club Aston Villa, who play in the Championship.
The 25-year-old joined the Swans five months after his elder brother Andre departed the club.
"I think I made a wonderful choice," Ayew told Swans TV.
“I need stability and I think this is the perfect place for me to grow and improve in a lot of aspects.
“I am so grateful to be here. It’s the next step in my career.
“I have been here several times in the past with my brother and I saw a lot of positive things.
“He spoke to me about the club and he said only good things. It didn’t take too long for me to make a decision.
“I always knew this team had quality players. The team had hard times last season, and this season didn’t start too well."
Ayew made his Swansea debut as a second half substitute in a 2-0 league triumph over Leicester City on Sunday.
The frontman moved to England in 2015 from French outfit Lorient, having earlier been on the books of Sochaux and Marseille.