England Under-21 defender Dawson was part of the Stuart Pearce's Team GB Olympic squad in the summer, but has made only three appearances for the Baggies this season, all in cup competitions.
One of those came against QPR in the third round of the FA Cup, meaning the 22-year-old is ineligible when Everton visit the Reebok Stadium on Saturday and must wait for next weekend's trip to Watford in the npower Championship to make his debut.
Wanderers boss Dougie Freedman told his club's official website: "I've worked very hard to try and get Craig to come on board. He had four or five different options and it's good news that he wants to come and play for us.
"When I spoke to him he indicated that he was very keen to come here.
"He made the decision, and fair play to West Brom for letting him make that decision, because he wants to come to a club where he feels he can improve.
"I want to sign players that want to be here and Craig has decided that this move gives him the chance to improve.
"That's exactly the kind of player I want."
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- Stuart Pearce