The 21-year-old has made just 11 appearances in La Liga this campaign – including nine off the bench – and netted three goals.
The Premier League club have agreed a €500,000 (£410,000) loan fee, with another €100,000 (£82,000) in potential add-ons.
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"Thievy is a good striker. He is quick, can score goals and is able to play across the front three positions," the Spaniard told the club's official website.
West Brom's sporting and technical director, Richard Garlick, argues that Thievy will provide the team with something different up front.
"We're delighted to welcome Thievy to the club," he enthused. "We set out to strengthen our forward options and Thievy is a little different to the other strikers we have.
"He is a player we have been monitoring for some time and has arrived with a real hunger to prove himself in the Premier League."