The Londoners said on their website (www.arsenal.com) on Monday that the move on transfer deadline day was subject to regulatory processes.
The 30-year-old has played just seven times for the Gunners this season and was not included in the France squad that played Germany and England in November.
"I really need to play. (France coach) Didier Deschamps didn't call me for the last two games so it's obvious, I've got to play more than I do," Debuchy said in December.
"I need to have several games under my belt to be at the Euros. You can't be in the French squad if you play a game once a month or less than that."
France hosts the tournament from June 10 to July 10.
(Reporting by Alan Baldwin, editing by Tony Jimenez)
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