The 27-year-old spent the entirety of the 2013-14 campaign with the German club and made 24 top-flight appearances.
Hamburg coach Mirko Slomka revealed in April that a full-time deal had been agreed and Arsenal have now confirmed the transfer.
Djourou joined Arsene Wenger's side from Swiss outfit Etoile Carouge in 2003 and made 144 appearances for the London club.
However, he failed to establish himself as a first-team regular at the Emirates Stadium and enjoyed temporary stints at Birmingham City and Hannover before joining Hamburg in July 2013.
He was also part of the Switzerland squad that reached the last-16 stage of the recent World Cup in Brazil.
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