"We are very pleased that Bernd Leno will be joining us", Emery said on the club website "Bernd is a goalkeeper of high quality and experience".
Leno signed for Leverkusen in 2011 from Stuttgart and in September became the youngest goalkeeper to feature in a Champions League match at the age of just 19 years and 193 days, during a group-stage game against Chelsea.
The Gunners are yet to confirm the length of Leno's contract, but the 'keeper is expected to be viewed as a longterm replacement for Petr Cech.
He has also made six senior caps for Germany, and while he was selected in Jogi Low's preliminary squad for the 2018 World Cup, he missed the cut for the final 23-man panel.
The Uruguay global, now away on World Cup duty in Russian Federation, was first tipped to join the Gunners following Unai Emery's arrival last month.
The signing means that new Arsenal manager Unai Emery is already building a far more tenacious squad than the one which operated under the previous manager Arsene Wenger. Both goalkeepers have one year remaining on their contracts and, while Cech has generally been the number one, has had a mixed season.
"In Germany, Arsenal are so famous and when I heard it (transfer), I was a little bit nervous, but at that moment it was clear for me: I wanted to sign for Arsenal".
Arsenal have been in talks to sign the Uruguay global, although the deal is dragging out with the player competing at the World Cup in Russian Federation.
The Uruguay worldwide is now at the World Cup in Russian Federation with his national team, for whom he has four caps. With Leverkusen missing out on the Champions League, now was the ideal time for Leno to move on and prove himself somewhere else as one of Europe's best shot-stoppers. "Good luck in the future". Most of our media is owned by a handful of offshore billionaires with personal agendas.