Bade moves to Bayer for €25m and has signed a five-year deal to 2030.
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Bayer chief Simon Rolfes said: "In Loic Badé, we've signed a young but very experienced central defender for Bayer. He's used to playing against world-class attackers in the Spanish La Liga.
"Loic is physically demanding and knows how to read the game, a key addition to strengthening our defense. With this defense, we can compete at the highest level."
Meanwhile, Bade stated: "The Bundesliga and German football fascinate me greatly. Bayer Leverkusen have achieved great recognition abroad in recent years.
"I've seen them a lot on TV, especially in European matches. The stadium and the Leverkusen fans were fantastic. It will be great fun to fight for a trophy."