The striker penned a three-year deal at the City Ground on Tuesday after passing a medical.
The 25-year-old, who featured for Ireland at this summer's European Championship, becomes the latest Forest signing by new boss Sean O'Driscoll following the club's takeover.
Cox had struggled to earn a regular first-team spot at The Hawthorns and that challenge was likely to become more difficult this term following the arrivals of Markus Rosenberg and Romelu Lukaku.
In a statement on West Brom's official website, sporting director Dan Ashworth said: "I would like to place on record my thanks to Coxy for his great service to the club.
"He has a fantastic attitude which I think is best summed up by the fact he did not miss a single game through illness or injury.
"We've had lots of interest in him this summer and this is a good move for him and his career.
"He joins Nottingham Forest with our best wishes."