The contract is subject to the successful completion of a medical but provided all is well he will join Dexter Blackstock in pledging his future to Forest, the striker having extended his contract until the summer of 2017.
Forest chairman Fawaz Al Hasawi told the club website: "I'm delighted that Radi has joined Dexter in deciding his long-term future is with us at The City Ground.
"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 in a loan deal in 2009 before making the move permanent the following year.
He has scored eight goals in 68 league appearances for the Championship side.