The 32-year-old Dutchman was given permission to find a new club after Wales international Wayne Hennessey returned to full fitness and he decided to move on after 20 appearances in two years.
Boss Billy Davies is delighted to get an experienced keeper without having to pay a fee.
He told the club's official website: "Dorus is a very good signing for us. We have a good, young pool of goalkeepers at the club but he brings with him an abundance of experience which will be of benefit to everyone.
"He played a pivotal role in Swansea's meteoric rise through the leagues and was unfortunate not to get more games at Wolves.
"To sign a goalkeeper of his calibre on a free transfer is a great piece of business."
- Sports & Recreation