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The 25-year-old put pen-to-paper on a four-year deal at the AOL Arena at the weekend after the clubs agreed a €5million (£3.4million) fee.
Zidan joined Mainz from Werder Bremen in January and went on to score 13 goals in 15 Bundesliga matches.
He could not prevent Mainz from being relegated however, and Hamburg have pounced to keep him in the top flight of German football.
"We are delighted to have been able to sign Mohamed Zidan. He is a player we really wanted to have," HSV sport director Dietmar Beiersdorfer told the club's official website.
"Mohamed has proved his ability in the Bundesliga.
"His speed and his individual class will add a whole new dimension to our attacking game."