The full-back has completed his move to the Emirates Stadium as Newcastle confirm the arrival of his replacement, Daryl Janmaat, to become the club's second summer signing
The French full-back agreed a €10 million move to the Emirates Stadium earlier this month and underwent a medical, but completion of the deal was held up while Newcastle sought a replacement.
However, United have now finalised formalities following the signing of Netherlands international Daryl Janmaat on a six-year deal, allowing Debuchy to sign on the dotted line with the Gunners.
"We are delighted to welcome Mathieu Debuchy to Arsenal," Arsene Wenger told the club's official website.
"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 added: "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."
Wenger was searching for a replacement for right-back Bacary Sagna, who joined Manchester City on a free transfer earlier in July after telling the Gunners who would not extend his contract.
The France international becomes Arsenal second major signing of the summer following the €40 million arrival of forward Alexis Sanchez from Barcelona.