Celtic's reward for Saturday's 3-1 win at Partick Thistle is a trip to St Johnstone in the quarter-finals of the Betfred Cup while Rangers face Ayr United.
Current Ladbrokes Premiership leaders Hearts will host Motherwell while Edinburgh rivals Hibernian will welcome Aberdeen to Easter Road.
The League Cup ties are due to be played on September 26 and 27.
Steven Gerrard has urged Rangers to grasp the chance of a Hampden return after booking their place in the quarter-finals with a 3-1 win at Kilmarnock.
The Light Blues suffered agony on both their visits to Mount Florida last term, crashing out in the semi-finals of the League Cup to Motherwell before being humiliated in the William Hill Scottish Cup by a 4-0 Old Firm drubbing as they again fell in the last four to Celtic.
But with his new-look line-up continuing to impress, Gerrard wants Rangers to look ahead with optimism.
Gerrard - who side saw off Killie thanks to Alfredo Morelos' hat-trick - said: "We're happy with the draw. You always look for a home fixture.
"Ayr United will be pleased with it as well, the chance to come to Ibrox and get a scalp against us.
"It's a good draw for both teams and a tie we will look forward to. It was part of my team-talk to say to the players they are four games away from winning a trophy, three away from a final. You are close to getting to Hampden. That's exciting, an incentive.
"If we go and perform like we did today against Ayr United we have a chance of playing at Hampden. That will be big for my players."