The 34-year-old had made 145 appearances for the Swans since joining on a free transfer from Southend in 2008, and helped them win promotion to the Premier League through the play-offs in 2011.
But Gower has found opportunities limited since Michael Laudrup succeeded Brendan Rodgers and, having spent the latter part of the season on loan at Charlton, has decided to end his spell in south Wales.
"I'm sad to be leaving, but it is in the best interests of both myself and the club," he said.
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