Brendan Rodgers’ side demolished Inverness CT 6-0 on Saturday and they’ll welcome Championship opponents St Mirren next month. Jack Ross and his team were able to reach the last four after beating East Fife.
Elsewhere, the winner of the Hibs v Hearts replay will have a home tie against lower league opponents, as they’ll host either Ayr United or Clyde.
Quarter-final draw in full
Celtic v St Mirren
Aberdeen v Partick Thistle
Hearts or Hibs v Ayr United or Clyde
Rangers v Dunfermline or Hamilton
All quarter-final matches will be played on the weekend of 4 March.