Holders Celtic face a trip to play Partick Thistle as they begin their defence of the League Cup. The second round draw was held after Hearts defeated Inverness to qualify for the knockout stage and they were rewarded with a trip to Dunfermline.
There are three all-Premiership ties with Livingston drawn at home to Motherwell, Kilmarnock hosting Rangers and Aberdeen drawn to play St Mirren at Pittodrie.
Dundee play Ayr United at Dens Park, Hibernian have a home draw against Ross County, While St Johnstone face a visit to Queen of the South. 
Aberdeen, Hibernian, Celtic and Rangers were all seeded for the draw as Scotland's European representatives. Ayr United, Dunfermline, Livingston and St Johnstone were also seeds as the four group winners with the best record.
Dundee, Hearts, Kilmarnock and Motherwell were through but unseeded as the remaining group winners, with Partick Thistle, Queen of the South, Ross County and St Mirren the best four second-placed sides.
Matches are scheduled to take place on August 18.