The Greece international has been plagued by injuries and made only five appearances for Schalke last season due to a knee problem and then a dislocated shoulder, which ruled him out of the World Cup.
Papadopoulos was linked with a move to Liverpool, but the 22-year-old has now sealed a move to the BayArena for the upcoming campaign.
He told Leverkusen's official website: "I am very happy that it worked out with the change. Bayer 04 is a club just like Schalke with major international ambitions.
"Unfortunately I was injured more often in the past season. But now I'm back fit and highly motivated to achieve with Leverkusen both my personal goals as well as the club."
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