The former Leeds United goalkeeper has signed a two-year contract with the Robins.
The 31-year-old was released by the Whites at the end of the season, having also enjoyed spells with Barnsley, Sheffield Wednesday, Preston North End and Darlington.
"He has great experience - in the Championship and League One - and I am delighted to have him here," said the Swindon manager Danny Wilson.
"He will provide the keepers with good competition next season and is loud, has a big frame and will do a good job for Swindon Town."