The Ibrox side saw their promotion hopes crumble at the end of the 2014-15 campaign when they were beaten 6-1 on aggregate by the Fir Park side.
Manager Mark Warburton – who led Rangers back to the Ladbrokes Premiership after picking up the pieces of that play-off disaster – will now take his side back to Fir Park for their opening Group F clash on 16 July.
Rangers then host Annan three days later before facing East Stirlingshire – who have been relegated to the Scottish Lowland League – at Ochilview on 22 July.
Rangers’ final group game will be against Stranraer at Ibrox on 25 July. All but the Annan clash will be screened live on BT Sport.
Ray McKinnon’s first match in charge of Dundee United away to Arbroath on 15 July in Group C will also be shown live on the satellite channel as will the Group B match between St Johnstone and Falkirk on 23 July.
Holders Ross County will kick off the defence of their trophy with a trip to Montrose on 16 July.
The final round of group-stage games are scheduled to take place across the weekend of 30-31 July but are subject to TV selection.