The 28-year-old, who was part of the French World Cup squad which reached the World Cup quarter-finals, will present a ready-made Premier League replacement for Bacary Sagna, who earlier this summer left Arsenal to join Manchester City on a free transfer.
Debuchy, who has reportedly cost the Gunners around £12million, becomes Arsenal's second signing of the summer, following the arrival of Alexis Sanchez from Barcelona.
A post on Arsenal's official Twitter feed read: "It's official - Mathieu Debuchy has signed for @Arsenal!"
Debuchy told arsenal.com: "I'm very proud to be joining a great club like Arsenal and to wear its colours, it's one of the biggest clubs in the whole world.
"I'm looking forward to working with Arsene Wenger and to helping the team build on last season's FA Cup success. Playing again in the Champions League is a big excitement for me and I will do my best to help Arsenal compete for trophies."
Manager Arsene Wenger added: "We are delighted to welcome Mathieu Debuchy to Arsenal Football Club.
"He has shown he can perform at the highest level with his club sides and also for France. He is a quality defender who has good Premier League experience and I'm confident he will fit in very well with us."
Debuchy made 46 appearances in his 18 months on Tyneside after signing from Lille, where he won the Ligue 1 and Coupe de France double in 2010-11.
He was named in the Ligue 1 team of the season the following year, having also won the first of his 25 France caps in October 2011 against Albania.
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