The Dons ensured their place in the draw as a seed with a 3-0 win over Raith Rovers, a result which saw Queen of the South take the final spot.
Jim Goodwin’s men have been rewarded with a trip to Galabank to face Annan Athletic, the only team from League Two, while Doonhamers will travel to Ibrox to face Rangers.
Ross County have been impressive in the group stages and will host Celtic which is one of three all-Premiership ties. Hearts hosting Kilmarnock and Livingston v Dundee United the others.
Ties will take place August 30/31.
The Premier Sports Cup last-16 draw in full:
Rangers v Queen of the South
Partick Thistle v Arbroath
Motherwell v Inverness CT
Livingston v Dundee United
Dundee v Falkirk
Annan Athletic v Aberdeen
Hearts v Kilmarnock
Ross County v Celtic