The first leg ended 2-2 at Pittodrie, with FCSB squandering a 2-0 lead after Juri Cisotti’s red card.
FCSB boast strong European history, including the 1986 European Cup and 2006 Europa League semi-final run.
Aberdeen, 1983 Cup Winners’ Cup champions under Sir Alex Ferguson, still seek their first Europa League group-stage berth.