The Scottish giants are bidding to reach the league phase of the UCL after missing out last season following a shock penalty shootout loss at the hands of Kazakhstan side Kairat.
Following confirmation of the UEFA draw, Martin O'Neill's defending champions are at home in the first leg on August 18th or 19th, with a return game the following week.
LASK won their domestic title for the second time last season - their first since 1965 - which meant they qualified directly for the playoff round alongside Viking Stavanger and AEK Athens.
If Celtic progress, the league phase is due to start on September 8th, with the draw for that stage on August 27th.
O'Neill made the Europa League knockout playoffs last season - before being eliminated by VfB Stuttgart and Celtic have not reached the UCL knockouts since 2013 under former boss Neil Lennon.