The Germany Under-19 international has moved to the BayArena for a reported fee of €10m (£6.9m).
Tah, 19, spent last season on loan at Fortuna Dusseldorf.
"Jonathan Tah is a greatly talented central defender who was able to get some valuable match practice at Fortuna Dusseldorf last season and proved to be one of the pillars of that side," director of sport Rudi Voller told Leverkusen's official website.
"His signing is a great investment in the future, but Jonathan has the class to help us out immediately. There were many clubs interested in him and this makes us even happier that he has chosen Bayer Leverkusen."
Tah has made six appearances for Germany's Under-19 side.