The 30-year-old Argentina skipper was presented to the media on Thursday after putting pen to paper on a three-year contract.
"I am looking forward to playing for this fine club and the challenge of playing Bundesliga football," Sorin was quoted as saying on Hamburg's website.
The arrival of Sorin fills the gap left by Dutch international Khaled Boulahrouz who joined Chelsea and Daniel van Buyten who was sold to Bayern Munich.
"We are glad that we could sign Juan Pablo.
"He is an international player, and will bring a lot of experience to our side," said Hamburg's sporting director Dietmar Beiersdorfer of the defender who has reportedly cost Hamburg 2.5 million Euros ($3.21 million).
Sorin, who was capped 75 times by his country, captained Argentina in the 2006 World Cup finals where they were eliminated by hosts Germany in the quarter-finals.
Hamburg qualified to the group stage of the UEFA Champions League. They were drawn in Group G with Arsenal, FC Porto and CSKA Moscow.