Curtis joined the Swans from Wrexham hours before the transfer deadline in January 2012 for an undisclosed fee.
He signed a three-and-a-half year contract after catching the eye with his performances for the Blue Square Premier club.
The former England Under-19 and England C right-back started his career at Manchester City, featuring in their FA Youth Cup side alongside Micah Richards and Daniel Sturridge as they reached the final in 2006.
But after his release in 2009, Curtis went on trial at Wigan Athletic and Celtic before agreeing to move to the Racecourse.
His move to the Liberty saw him reunited with Neil Taylor, who he played alongside at both Manchester City and Wrexham.
However, the pacey defender has found first team opportunities hard to come by since arriving in SA1 and he spent time on loan at League Two clubs Fleetwood and York last season.