Switzerland international Djourou, 26, has signed for Bundesliga side Hamburg after the defender spent the second half of last season at Hannover.
Meanwhile 22-year-old midfielder Coquelin will also move to Germany, with Freiburg taking the former France Under-21 international to the Mage Solar Stadion for the forthcoming campaign.
Gunners' boss Arsene Wenger has already allowed several players to leave at the expiration of their contracts, with the likes of Andrei Arshavin and Denilson moving on.
Goalkeeper Vito Mannone has also been sold to Barclays Premier League rivals Sunderland while former Auxerre forward Yaya Sanogo remains the only signing to date, with a deal for Real Madrid's Gonzalo Higuain still yet to come to fruition.
Source: PA
Source: PA