The Reds were paired with Besiktas in Monday's draw in Nyon, conducted by UEFA's Europa League final ambassador Jerzy Dudek - Liverpool's goalkeeper in that famous penalty shoot-out win over AC Milan
For Celtic, the draw marks a reunion with the opposition for the most famous match in the club's history, the 1967 European Cup final which Jock Stein's 'Lisbon Lions' won 2-1
Tottenham will also face Italian opposition in the form of Fiorentina, while Everton were drawn against Swiss side Young Boys in the first tie out of the UEFA pots
Sevilla, the competition's last ever defending champions as this season's winners will instead qualify for the Champions League, face Bundesliga side Borussia Monchengladbach.
The tie pits together teams who have won the competition, or its predecessor the UEFA Cup, five times between them.
Remarkably, aside from the ties involving Celtic and Liverpool, only one other features teams who have played against each other before - Villarreal and Salzburg, who met in the the 2009-10 group stage with Salzburg winning both games.
Liverpool won their last meeting with Besiktas 8-0 in the 2007-08 Champions League
Current captain Steven Gerrard scored in the game but the other goalscorers - Yossi Benayoun with a hat-trick and Peter Crouch and Ryan Babel netting twice apiece - have long since departed Anfield.
The first-leg matches will be played on February 19, with the return fixtures seven days later.
Source : PA
Source: PA