The Reds have paid an undisclosed fee for the Republic of Ireland international striker, who has signed a three-year contract.
Forest Chairman Omar Al Hasawi said: “Sean O’Driscoll highlighted that he wanted to bring in a man with a proven goal-scoring record and Simon has that pedigree.
“I am sure he will prove to be an excellent addition to our squad as we look to take the Club forward.”
Cox launched his career with his home-town club Reading but was restricted to just nine substitute appearances.
After loan spells with Brentford and Northampton his career gathered pace where Swindon as he scored 42 league goals in 80 appearances.
He clinched a big money move to West Brom in 2009 and scored 18 league and cup goals for The Baggies.
Cox qualifies for the Republic through his Irish-born grandmother and has scored three goals in 14 appearances for his country since making his international debut last year.
He figured in all three of Ireland’s group game at Euro 2012.