Heynckes’ last time as coach was as caretaker at Bayern Munich after the sacking of Jurgen Klinsmann last season.
The 64-year-old will replace Bruno Labbadia, who has joined Hamburg.
Heynckes said: “Leverkusen’s approach gave me pleasure, all the more so as I realised when I was at Bayern that I still had the desire. That’s why I accepted the mission.”
