The Switzerland central midfielder has agreed a five-year contract, the day before the English club hope to finalise a club-record £105m deal for Declan Rice.
Xhaka, 30, played 297 times in all competitions for the Gunners, scoring 23 goals, after signing from Borussia Monchengladbach in summer 2016.
Briefly captain for the north London side, he had a year left on his previous contract but was expected to leave in this transfer window given Arsenal’s move for Rice and their desire to raise funds.
He said: ‘I know the league inside out and I watched it when I was in London. Bayer 04 is a club with an impressive history and ambitious targets.
‘Above all, I see it as a club with a great future. Discussions with the management have been incredibly motivating. Everybody here is ambitious and wants to achieve something – I’m very much looking forward to the next few years.’
Leverkusen sporting managing director Simon Rolfes added: ‘In Granit we have been able to bring in an absolute top player.
‘His ability on the pitch is well known. But, above all, there are few players who are able to so convincingly lead a team like he does thanks to his outstanding mentality and personality.’
Xhaka won two FA Cup titles and helped Mikel Arteta’s men finish second in the Premier League behind Manchester City last season.
Ajax defender Jurrien Timber is scheduled to have a medical on Friday morning ahead of completing his £40m move to Arsenal.
Rice will also undergo his medical on Friday before finalising his record £105m transfer from West Ham.