The Polish playmaker has put pen to paper on a three-and-a-half year deal, subject to successfully completing a medical.
Majewski, 26, follows striker Dexter Blackstock, who recently agreed new terms to keep him at the City Ground until the summer of 2017, in committing his long-term future to the club.
Forest chairman Fawaz Al Hasawi said: "I'm delighted that Radi has joined Dexter in deciding his long-term future is with us.
"It proves that players want to be a part of what we are trying to achieve for the club."
Majewski joined Forest from Polonia Warsaw on loan in 2009 and completed a permanent switch to the east midlands a year later.
He has scored eight goals in 68 league appearances, including spectacular strikes against West Brom and Derby and a hat-trick against Crystal Palace.
- Sports & Recreation
- Dexter Blackstock