Neil Lennon's side beat NSI Runavik 6-4 to complete a 12-5 aggregate victory and now face Asteras Tripolis of Greece, with the first leg at Easter Road on Thursday July 26.
Hibs were 2-0 down inside five minutes but goals from John McGinn, Lewis Stevenson, David Gray, Efe Ambrose and a Stevie Mallan double saw the visitors come out on top.