The England international was ruled out for 12 weeks after suffering a stress fracture to his right foot, with Boaz Myhill and Luke Daniels left to fight it out for the gloves.
And they have now been joined by former Norwich City man Camp, who has signed a rolling monthly contract at the Hawthorns.
Camp left Carrow Road at the end of last season, following a six-month stay that had seen him fill in for another England keeper in John Ruddy.
"Lee will bring experience and authority to the goalkeeping department," West Brom goalkeeping coach Dean 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."
