The 27-year-old has been with the German side on a season-long loan and is expected to end his 11-year affiliation with the Gunners to make a permanent move to the Bundesliga
The Switzerland international joined the Bundesliga side in a temporary switch from the Gunners in July, though the deal was reported to include a clause allowing the German outfit to buy him outright.
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"I am happy that he's staying with us for the next few years as he's a stabilising influence at the centre of our defence," the 46-year-old coach told reporters.
No details of the deal have been released, although local media reports have indicated that Djourou has agreed a contract that will keep him with Hamburg until 2016.
The Swiss defender has made 22 appearances for Hamburg this season but has been unable to prevent them from enduring a nightmare campaign, currently sitting second from bottom of the Bundesliga with six games to play.