Mark Hughes' side, who qualified due to their impressive disciplinary record, will take on Danish side FC Midtjylland while Intertoto Cup winners Villa face Icelanders Hafnarfjordur.
Queen of the South will play Danish outfit Nordsjalland after reaching this stage by virtue of their inspiring run to the Scottish Cup final last season, where they lost to Rangers.
Irish outfit St Patrick's Athletic, who beat Latvian side JFK Olimps Riga in the first qualifying round, face a difficult task against experienced European campaigners Elfsborg of Sweden.
Villa put themselves into the hat by defeating Odense BK in the Intertoto Cup at the weekend.
On Thursday night, Martin Petrov and Darius Vassell scored against Faroe Islanders EB/Streymur at Barnsley's Oakwell ground as they won 2-0 on the night, 4-0 on aggregate.
St Patrick's eased through the first qualifying round with a 3-0 aggregate win over JFK, winning the home leg 2-0 this week.