The 22-year-old heads to the German side as a free agent having left Marseille once his contract expired earlier in the summer.
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Nadir was a bit-part player for the French club, starting just five of his 20 Ligue 1 games, scoring zero goals but providing four assists.
"I'm very happy to be a HSV player now. I can't wait to meet the HSV fans and play for Hamburg," Nadir told the club’s website.
Sporting director Claus Costa added: "Bilal has a lot of quality and is technically very strong."