Rangers’ reward for knocking out Premier Sports Cup holders St Mirren is a mouth-watering quarter-final against Old Firm rivals Celtic.
Derek McInnes earned his first win as boss with a thumping 5-1 victory on Sunday and will now host Celtic.
Stenhousemuir, who stunned Motherwell in extra time, will host last season’s Scottish Premiership runners up Hearts.
Aberdeen will go to Kilmarnock in an all top-flight tie, while Ross County welcome Hibernian to the Highlands.
The games will be played across the weekend of 12-13 September.
McInnes’ first taste of an Old Firm game as Rangers manager was due to be at Celtic Park on Sunday 20 September but will now be across the city.
Kilmarnock were the first team into the last eight after beating Ayrshire rivals Ayr United in a five-goal thriller.
Aberdeen overcame Dundee 3-0 at Pittodrie on Saturday, Ross County beat Dunfermline 2-1, while Celtic trounced Dundee United 4-0 at Tannadice.
