The France international has put pen to paper on a long-term contract after the two clubs agreed an undisclosed fee, which is reported to be in the region of £12m.
Debuchy is said to have been identified as a summer target for the North London outfit after full-back Bacary Sagna opted to leave Arsenal for Manchester City on a free transfer.
"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," Debuchy told the club's official website.
"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 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 joined Newcastle from Lille last year.