The 32-year-old would have started the season as the Potters' third-choice goalkeeper behind Denmark international Thomas Sorensen and Asmir Begovic.
Simonsen played 187 games for Stoke and helped the Potters win promotion to the Premier League in May 2008.
The former Tranmere and Everton stopper fell out of favour following Sorensen's arrival in August 2008 and spent the last two months of last season on loan at Sheffield United.
Manager Tony Pulis told the club website: "There was a clause in his contract which allowed him to move on a free if he received the right offer.
"He did well in his time at Sheffield United when he went out on loan in search of first-team football and that has led to this chance.
"'Simmo' came to the club in my first spell as manager and has been a great servant throughout his time here, playing a big part in us winning promotion, so we would like to thank him for his contribution and wish him well."
Source: BBC Sport
Source: BBC Sport