The 29-year-old made 11 appearances on loan with the Cherries and has now penned a two-and-a-half-year deal after his contract at The Hawthorns expired.
Camp has a wealth of experience having made more than 350 league appearances and has also played for Derby, Burton, QPR, Norwich and Nottingham Forest.
He told the club's official website: " I am pleased everything has been sorted and I am delighted to have signed.
"Discussions have been ongoing for the past couple of weeks but we have come to a pretty speedy conclusion in the end, so credit must go to the football club for how they have handled it.
"Going into the Brighton game we weren't a million miles apart. If anything slowed it down over the Christmas period it was the fact we had three games in six days.
"I spoke to the manager at the hotel before the game on New Year's Eve and I was fairly confident we would all get to where we needed to get to, to make the deal happen.
"Now I have something sorted, I can concentrate on playing football."