Debuchy, 30, was linked with a move to Die Werkself in late January after Kicker reported that there was interest from Roger Schmidt’s side.
Debuchy will link up with former Bayern Munich defender Diego Contento at the French side.
The Frenchman moves on from the Emirates Stadium in a bid to state a claim for a potential place in Didier Deschamps’ Euro 2016 team.
To break into Deschamps’ squad, Debuchy will have to outplay veterans Bacary Sagna and Olympique Lyon’s Christophe Jallet who are both two-years older than Debuchy.
Kicker report that the bid for Debuchy failed to materialise because of the talent Tin Jedvaj possesses in that right-back position after he proved himself since the Rückrunde.