Delap originally had a spell on loan at Stoke from October 2006 before making his move permanent three months later as Tony Pulis assembled a squad that would win promotion to the Premier League the following season.
The Republic of Ireland international has been on loan with Barnsley since January, where he played his part in maintaining the club's Championship status.
Delap revealed he had already decided it was time to leave the Potters during last season, and his biggest regret was not being able to acknowledge the club's supporters for their backing.
"I am a little sad I didn't really get the chance to thank the Stoke fans that supported me and the team so loudly during the rise of the club over the last seven years," Delap said.
"It seems the club is going in another direction but for me having not featured much this season I already knew it would be time for me to move on.
"I have proved to myself and others that I can still play at a high level after playing a part in Barnsley's survival this season and I feel fit enough to play on for another couple of seasons.
"It's a shame what has happened there this week as Tony has done a huge job in his tenure and rewind seven years everyone there would have bitten your arm off to be they are now.
"Having said all that Stoke City will always be a massive part of my life and I hope me in theirs, I am sure our partnership will be fondly remembered."