Morton will take on Aberdeen at Hampden on Saturday 22 October in the first last-four tie. The game will be shown live on BT Sport and will kick off at 12.15pm.
The following day the national stadium will host Rangers v Celtic. Again the match will be live on BT Sport, with kick off scheduled for 2.15pm.
Ticket allocations and pricing will be announced at the beginning of next week.
Morton, who knocked out Dundee United in midweek, are playing in their first League Cup semi-final for 37 years.
Aberdeen, who won the tournament in 2014, booked their place in the semis with a last-minute win over St Johnstone.
Rangers and Celtic meet in a repeat of the League Cup semi-final of two years ago when Ronny Deila’s side won 2-0.
Rangers won through to the last four with a comfortable 5-0 quarter-final victory over Queen of the South.
Celtic defeated Alloa 2-0.
The final of the 2016 Betfred Cup will take place on Sunday 27 November at Hampden.