The first leg will take place at Celtic Park next Thursday night, March 11th, with the return leg in the Nou Camp taking place two weeks later, Thursday 25th March.
It is not yet known how many tickets will be available for Celtic supporters for the game.
If Celtic beat Barcelona, we will meet either Roma or Villareal in the quarter finals. The winners of that game will play either Genclerbirligi or Valencia in the semis.
The full draw for the Fourth Rounf is listed below.
Celtic v FC Barcelona
Genclerbirligi v Valencia
Bordeaux v Club Brugge
Newcastle Utd v Real Mallorca
Auxerre v PSV Eindhoven
Inter Milan v Benfica
Liverpool v Marseille
Villareal v Roma