Thelin, 26, came to attention with 19 goals in a spell at Waasland-Beveren last season.
Leverkusen have now swooped to snare Thelin as a rival for Lucas Alario and the injured Joel Pohjanpalo.
"He has developed excellently in the Belgian league," head coach Heiko Herrlich said of the rangy forward.
"Isaac is an additional option for our offensive play. It will make us even more variable in attack."
Thelin will wear the number 11 shirt vacated by retired club favourite Stefan Kiessling.