The experienced Palop, who won the 2006 and 2007 UEFA Cups with the Spanish club he joined in 2005, received a one-year deal to 2014.
"After all the years in Spain's top division, I am delighted to be getting the chance to play abroad," Palop, who was in the Spain squad that won Euro 2008, said in a statement.
Leverkusen, who have keeper Bernd Leno as first choice, finished third in the Bundesliga and will compete in next season's Champions League group stage.
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