The shot stopper earned a summer transfer to the Gunners by impressing on loan last season.
Now he has signed from Brentford for a mega £27million after he claimed the no.1 shirt at the Gunners last term.
Arsenal sporting director Edu said: "We are so happy to have completed the deal to sign David from Brentford.
"He had a beautiful first season with us, winning the Premier League Golden Glove. He is a talented international, a great professional and a popular figure at the club. We benefited from all of this last season during his loan with us.
"David's signing is another strong example of our recruitment strategy in action, as we continue to build a team that will challenge for major trophies.
"We know there's so much more to come from him and we are excited that he will continue to be a big part of the journey we are all on."
Arsenal manager Mikel Arteta said: "David showed us last season what an important player he is for us, so we are delighted he is now officially our player.
"He is a big presence in our dressing room and we are really pleased to keep working with him.
"We know he will take the strong foundations he put in place last season and build on them in the years to come, and that he will enjoy more success with us.
"We have a very talented group of goalkeepers and I love to see connections like the one I see in our goalkeeping unit."