The Spaniard, who won La Liga twice with Valencia, has been with Leverkusen since last summer after departing Sevilla, where he had spent eight seasons.
"Thanks to all my clubs, teammates, coaches and directors for their confidence," Marca quotes the 40-year-old as saying.
"It was an extraordinary experience. I've been privileged to have lived through unforgettable moments for every club I played for."
Palop was also part of the Spain squad that won Euro 2012.