The protracted transfer of the France international, understood to be worth around £12m, was finally confirmed on Thursday evening when Newcastle were able to announce the signing of Netherlands defender Daryl Janmaat from Feyenoord.
Debuchy, 28, is seen as a Premier-League ready replacement for Bacary Sagna, who left to join Manchester City on a lucrative free transfer after helping Arsenal beat Hull in extra-time at Wembley.
Arsenal have already brought in Chile forward Alexis Sanchez from Barcelona, with more additions expected ahead of the Community Shield on 9 August.
Debuchy is in no doubt he has joined a club very much on the up.
"I know that Arsenal can win titles every year. Winning the FA Cup last season was something magnificent, but I hope that it is just the beginning and that there will be more to come next season," Debuchy said in an interview with Arsenal Player.
"There are some really great players in this team. We saw that last season and I think it will be even better this season. I hope there is more silverware to come in the next few years."
Debuchy is confident he can continue his progress, having been a consistent performer at Newcastle following a £5m move from Lille in January 2013.
"The settling-in period will be easier. I have been playing in the Premier League for a year-and-a-half now, so I already know it well, so that will be in my favour."
Debuchy paid tribute Newcastle fans.
He added: "It was an extraordinary experience at a club with great fans. I thank them from the bottom of my heart because they really supported me during my time there and I hope they understand that I had a huge opportunity which I simply could not refuse.
"Playing again in the Champions League is a big excitement for me and I will do my best to help Arsenal compete for trophies."
Debuchy was part of the France squad which reached the quarter-finals at the FIFA World Cup™, where they were beaten by eventual champions Germany.
Gunners boss Arsene Wenger is confident his countryman will prove a neat fit into the team, where he will contest the right-back place with England hopeful Carl Jenkinson.
"The obvious replacement for Sagna was Debuchy," Wenger said. "He knows what to expect and that's of course a huge advantage.
"Debuchy is very good going forward, is very quick in transition. He is sharp in his marking, good with interceptions and quick to go from defence to attack.
"You feel he always has the desire to go forward, so I believe he will be perfectly suited to our style in that aspect."