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.
He spent much of his youth career at Stuttgart, but moved on in 2011 without taking in a first-team outing.
History was made that same year as he became the youngest goalkeeper to feature in the Champions League at 19 years and 193 days – in a meeting with Chelsea.
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.
Stephan Lichtsteiner has already been acquired to bolster the club’s defensive unit, and Goal has revealed that a deal for Sampdoria midfielder Lucas Torreira is also on the cards.