Stanisic, 23, completed a medical on Sunday.
German media reported the defender had joined Leverkusen without an option to buy.
"The team is full of top players and my conversations with the club have given me extreme motivation" Stanisic said in a statement.
"Josip Stanisic is already very experienced in the Bundesliga and Champions League. He is strong in his technique, intelligent, can play with both feet and versatile in defence," Leverkusen sporting director Simon Rolfes said in a statement.
Employed either as a wide defender or as a centre-back, Stanisic was born in Munich and came through the Bayern junior system.
