Goal revealed earlier on Tuesday that a deal for the 26-year-old was close , and that agreement has now been pushed through.
It is understood that the Gunners have invested €22m (£19.2m/$25m) in a new No. 1, with Unai Emery moving to strengthen the squad inherited from Arsene Wenger.
Petr Cech has been Arsenal’s last line of defence for the last three seasons, but the veteran Czech is now 36 years of age.
Emery told the club’s official website on landing a proven performer to take over between the sticks: “We are very pleased that Bernd Leno will be joining us.
“Bernd is a goalkeeper of high quality and experience. He has been a top performer and regular number one goalkeeper with Leverkusen in the Bundesliga for the past seven years.
“We are all excited that Bernd has chosen Arsenal Football Club and look forward to start working with him in pre-season.”
Leno moves to Emirates Stadium after seven years with Leverkusen which delivered over 230 Bundesliga appearances.
He spent much of his youth career at Stuttgart, but moved on in 2011 without taking in a first-team outing.
Quickly establishing a reputation as a reliable custodian, a senior international debut for Germany was made in 2015.
He now has six caps to his name, but was overlooked for World Cup 2018 duty this summer.
His absence from that tournament will allow him to settle in north London ahead of the new Premier League season.
Arsenal will open that campaign against reigning champions Manchester City , with it possible that Leno could be handed the toughest of tests on his competitive debut.
He will be relishing that challenge, with there still the promise of more additions to come at the Emirates.