The 25-year-old centre-back moves to the Bundesliga after only featuring twice for the Gunners this season, and having not played in the Premier League during this campaign
The 25-year-old centre-back has only made two appearances in total for Arsene Wenger's team this season in the Capital One Cup, with Thomas Vermaelen, Laurent Koscielny and Per Mertesacker all ahead of him in the pecking order.
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A statement on Arsenal's official website read: "Everyone at Arsenal would like to wish Johan well for his time in Germany."
Djourou is currently contracted to Arsenal until 2015, but Hannover are hopeful a permanent deal can be agreed at the end of the season if the player performs well in Germany.