New Wolves manager Kenny Jackett is looking to cut the wage bill at Molineux and he had informed the 32-year-old Dutchman that he could leave the club if a suitable offer was made to him.
A return to his native Holland was mooted at one stage for De Vries, but he will now stay in England after agreeing personal terms with Forest and passing a medical at the City Ground.
De Vries is vastly experienced when it comes to life in the Football League, having made close to 200 appearances for the Swans, but he found regular football hard to come by during a two-year spell at Wolves.
Forest manager Billy Davies 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."