Leno, 26, was joining a Gunners now under the control of new boss Unai Emery, who succeeded the long-serving Arsene Wenger at the north London club after the Frenchman stepped down at the end of last 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." Leno added: "I'll try to help the team to come back to the Champions League and to win some trophies. Arsenal belong in the Champions League.
"Now it's a new chapter for the club. I spoke to Unai Emery and he said that he believes I'm a good goalkeeper, and that he wanted me to join."
Emery said Leno was a "goalkeeper of high quality and experience", and he will now join a squad where veteran Petr Cech and David Ospina, playing for Colombia at the World Cup, have been the first-choice keepers.
The Gunners, who finished sixth last season, had previously signed Swiss defender Stephan Lichtsteiner on a free from Juventus, while midfielder Granit Xhaka extended his contract.
Nevertheless, Wenger's assistant Steve Bould, a former Arsenal defender, will remain on Emery's team.
Lehmann, a member of Arsenal's 'Invincibles', who won the 2003/04 Premier League title and went 49 league matches without defeat, did not go quietly.
Instead the former Germany keeper wrote on Twitter: "Dear #Arsenal Fans, I am sorry to leave the club after only one year again.
"It was a good experience working with the players as one of the assistant-coaches. But the attitude from our 2004-group is not needed there anymore."
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