The Baggies' goalkeeping coach Dean Kiely revealed his happiness at securing Camp, who was a free agent after leaving Norwich at the end of last season.
"Lee will bring experience and authority to the goalkeeping department," Kiely told the club's official website.
"We have acted quickly in the wake of Ben's injury and made a really good signing.
"Lee comes with a strong pedigree, having played at a high level both domestically and internationally.
"He ticked a lot of the boxes we required when we began the search for another keeper."
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