The versatile midfielder spent two years at Napoli - helping the club clinch the Coppa Italia last season - but will make the switch to Hamburg for his first taste of the Bundesliga.
Formerly of West Ham, Lazio and Fiorentina, Behrami makes the move to the Imtech Arena where he will be tasked with helping the club build on a woeful 2013-14 season.
Hamburg - ever-present in the German top flight - almost suffered relegation last term and Behrami spoke of his desire to impress at his new club.
"I already feel very good and am satisfied," he told Hamburg's official website.
"Hamburg is a new experience for me and a great club. It is a very important moment in my career
"After the World Cup I had about three weeks of vacation, so I've trained just seven days with the team.
"I must begin work on my fitness, but I'm here now. I need a little more time, but we have that time, so that is OK."
The move was finalised on Saturday, with Napoli confirming the completion of a final document.
On Twitter, Behrami thanked fans of the Italian club, writing: "You are unique in every way, as in any gesture I heard your love for this shirt and your city.
"I just tried to honour and respect it.
"Now I hope you can finally make your dream come true and win the Scudetto!"
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