Craig Levein’s men advanced to the last eight after Olly Lee’s goal was enough to defeat Dunfermline at East End Park on Saturday afternoon.
The Tynecastle club will look to make it to their first semi-final of any cup competition since they were defeated on penalties by Inverness in the 2013/14 season.
In doing so, they’ll have to defeat the side who knocked them out of the Scottish Cup at the quarter-final stage last term.
Hibs, meanwhile, will host Aberdeen after defeating Ross County 3-2 on Sunday afternoon.
Neil Lennon’s team made it to the semi-finals last season, where they lost 2-1 to eventual winners Celtic.
The holders will travel to St Johnstone as they look to keep up the defence of their trophy following yesterday’s 3-1 win over Partick Thistle.
Rangers host Ayr United at Ibrox after dumping Kilmarnock out of the competition in front of the BT Sport cameras.
The quarter-final matches will be played on the midweek of September 25/26.
The draw in full ...
Rangers v Ayr United
St Johnstone v Celtic
Hearts v Motherwell
Hibs v Aberdeen