The 38 SPFL teams not involved in Europe are included along with Lowland League side East Stirlingshire.
Teams were drawn into eight groups of five, split into north and south, with the first ties on 16 July.
The stand out tie sees Rangers face Motherwell.
Lowland League champions Edinburgh City, who beat Shire in their play-off to win promotion to League Two for the first time, will face Hamilton Academical, St Mirren, Livingston and Ayr United.
Now renamed the Betfred Cup, the group winners and four best runners-up progress to the second round when Celtic, Aberdeen, Hearts and Hibernian will join.
The final will be played at Hampden Park on 27 November.
Replays have been scrapped with any game ending in a draw going straight to penalties and the winner of the penalty shoot-out awarded a bonus point.
Group A: Dundee, Dumbarton, Peterhead, Forfar Athletic, East Fife
Group B: St Johnstone, Falkirk, Brechin City, Stirling Albion, Elgin City
Group C: Inverness Caledonian Thistle, Dundee United, Dunfermline Athletic, Arbroath, Cowdenbeath
Group D: Ross County (holders) Raith Rovers, Alloa Athletic, Cove Rangers, Montrose
Group E: Partick Thistle, Queen of the South, Stenhousemuir, Queen’s Park, Airdrieonians
Group F: Motherwell, Rangers, Stranraer, East Stirlingshire, Annan Athletic
Group G: Hamilton Academical, St Mirren, Edinburgh City, Livingston, Ayr United
Group H: Kilmarnock, Greenock Morton, Berwick Rangers, Albion Rovers, Clyde