The Republic of Ireland striker has signed a three-year deal with the club after passing a medical this afternoon and becomes the club's seventh signing of the transfer window
Cox signed a three-year deal with Forest after learning that he may find limited opportunities for first-team football at the Hawthorns, with the Baggies bringing in Markus Rosenberg on a permanent deal and Romelu Lukaku on loan from Chelsea.
The 25-year-old becomes the Championship side's seventh summer signing after the purchases of Adlene Gedioura, Danny Collins, Greg Halford, Dan Harding, Simon Gillett and Daniel Ayala.
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"The history of the club sells itself and I had a chat with [manager] Sean O'Driscoll and liked what he had to say.
"I also met the chairman the other day and had a good look around the facilities and can tell it's a club going forward.
"One of the most important things for me were the assurances I was given by the owners. I've seen enough in football where owners come into the clubs, have a little flutter and then go away.
"I wanted to make sure that they are going to be here for the long haul and they assured me that they are. They have big plans for the club and I want to be a part of that."Cox, who represented the Republic of Ireland at Euro 2012, will now seek to rebuild his career at the City Ground after an unsuccesful stint at the Hawthorns following his move from Swindon in 2009.
And Baggies sporting director, Dan Ashworth, expressed his belief that the move is good for all parties, saying: "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."
Forest chairman Omar Al-Hasawi was equally singing the praises of his side's new signing, saying: "I am sure he will prove to be an excellent addition to our squad."