The Bungesliga outfit swooped for the Switzerland international earlier this month, bringing an end to Behrami's two-year stay with Serie A side Napoli - whom he helped win the Coppa Italia last season.
After Hamburg came close to suffering relegation from Germany's top flight last term, head coach Slomka has been keen to strengthen his squad throughout the close-season.
Behrami featured for Hamburg against former club Napoli in a friendly on Friday and, though the Italians triumphed 2-0, Slomka believed his new midfielder displayed the attributes he is looking for.
"Valon is aggressive," Slomka is quoted as saying by Bild. "The opponents bounce off him. He is a mature athlete who signals to the enemy 'do not come near me'.
"That's why we brought him to us."
Hamburg director Dietmar Beiersdorfer was also glowing in his appraisal of Behrami, adding: "Valon has a great mentality.
"He is an experienced player. For us, the right man in defensive midfield."
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