The Ghanaian joined the Jack Army in January, but after drawing blank in 13 matches, made amends on the last day of the season with his side's equalizer in Sunday's 2-1 victory over West Bromwich Albion.
He made 14 league appearances involving nine starts over the campaign for Paul Clement's outfit, who are equally elated to have finished the season on 15th position after a fierce relegation battle.
“I was really, really pleased to get my first goal,” Ayew said, according to his club's official website.
“I think the supporters, the staff – everybody in the club was behind me.
"The only thing I could do to pay them back was to score a goal, so I am really happy I could do that against West Brom.
“My family were at the game too, so that made it even sweeter. It’s an amazing feeling to be safe, to go on holidays with this good feeling.
“I have to join up with my national team but I have one week off and I can enjoy it now. Then I will come back fresh next season.”
Ayew, who also assisted three goals, joined Swansea from championship club Aston Villa after struggling for playing time at Villa Park.
He netted nine times in 51 league games in two seasons for the Claret and Blue Army after transferring from French Ligue 1 side Lorient in 2015.
The 25-year-old also played for Marseille and Sochaux in the French top division.