Fulham will take on Faroe Islands side NSI Runavik in the first qualifying round of the Europa League.
The Cottagers will play the first leg at Craven Cottage on 30 June, with the return match played on 7 July.
If the London side come through the tie they will face Belfast club Crusaders in the second qualifying round.
Dundee United drew Slask Wroclaw in the second qualifier, with the first leg in Poland on 13/14 July before they meet at Tannadice on 21 July.
Fulham, finalists in the competition in 2010, earned their place in the draw via the Uefa Fair Play League and the ties will be new boss Martin Jol's first competitive games at the helm.
The first round qualifying draw in Nyon, Switzerland, threw up an all-British affair as Northern Irish side Cliftonville were paired with TNS from Wales.
League of Ireland Premier Division side St Patrick's Athletic will face Icelanders IBV, while Neath take on Norwegian club Aalesund and Glentoran play FK Renova of Macedonia.
In the second qualifying round, Dublin side Bohemians will go to either Siroki Brijeg or Olimpija Ljubljana, while Llanelli of the Welsh Premier League are at home first against the winners of the game between Dinamo Tbilisi and Milsami.
FA Cup finalists Stoke will enter in the third qualifying round, together with Scottish Premier League side Hearts, while Celtic go straight in at the play-off stage with Birmingham and Tottenham.
In the Champions League second qualifying round, Linfield will play FC Bate Borisov of Belarus, Bangor City take on Finnish side HJK Helsinki and Shamrock Rovers were paired with FC FLora Tallinn of Estonia.