Leno, omitted from the 23-man World Cup finals squad, will join the north London club next month when the transfer window opens.
The deal includes another £3m in bonuses which could be payable, depending on Arsenal’s success while Leno is at the club.
With both Petr Cech, 36, and David Ospina, 29, out of contract next summer, it’s not immediately clear which of the pair will be leaving this summer.
Napoli are keen on a season-long loan deal for the former Chelsea goalkeeper while Fenerbahce were reported to have agreed personal terms with the Colombian at the end of May.
Leno made 304 appearances for Bayer having begun his career with VfB Stuttgart II. With 51 appearances in the Champions and Europa leagues, the German ticks boxes for an Arsenal defence which lacked leadership over recent seasons.
With Sokratis and Lucas Torreira set to join as well, the Gunners now need to sell if they are to invest further in their squad. Earlier this summer claims circulated that Arsenal had a £50m transfer budget which Stan Kroenke increased to £70m and is now mostly spent on the three players.