A statement on the official Arsenal website read: "Everyone at Arsenal would like to wish Johan well for his time in Germany."
Djourou's move to Germany is dependent on the formality of the necessary paperwork being completed as he has already passed a medical.
" Johan Djourou is an internationally-experienced footballer who we are convinced will be able to help us out quickly," said Hannover's director of sport Jorg Schmadtke.
"He fits the bill perfectly for what we were looking for because he is also eligible to play for us in the UEFA Europa League."
"With his physical robustness, his tactical understanding and his high level of commitment, I am convinced we will profit from having him."
Hannover are currently 11th in the Bundesliga.