The Ireland international revealed on Twitter that he has signed a contract with the Championship club, and also thanked fans of his former side for their support
The 26-year-old Ireland international has agreed personal terms with Forest, who have met West Brom's valuation after the two clubs played a friendly on Thursday, with the Premier League side winning 2-0.
Cox announced the news himself on his Twitter page: "Think I'm all done now. Signed now. Can't wait to get started and exciting times ahead. #nffc.
"I would like to thank all the fans and players and staff at WBA for my time there loved it. Met some lovely people. Wish u all the best."
Baggies manager Steve Clarke revealed that Cox was left out of the side due to a bid being accepted by the Premier League club.
West Brom recently completed the signing of Chelsea striker Romelu Lukaku on loan for the season, as well as Markus Rosenberg on a permanent deal, and still have Peter Odemwingie, Shane Long, and Marc-Antoine Fortune as recognised strikers in the first team.