The veteran has signed a two-year deal with Bayer, moving to Germany as a free agent after coming off contract at Real Madrid.
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Vazquez passed his medical yesterday ahead if penning terms.
"My discussions with the management confirmed what I've been told - the club are absolutely focused on winning, are hungry and they are aiming for the biggest targets," said Vazquez.
"That mindset coincides with my ideas and I'm looking forward to striving for more success at Leverkusen."
Vazquez made 402 appearances and won 20 trophies at Real, including the Club World Cup three times.