Neilson left his head coach role at the Gorgie Road club in order to take over MK Dons in England's League One. He lasted just over a year down south before exiting in January 2018. He was hired by United in October of last season but was unable to guide the club back to the Premiership, losing on penalties to St Mirren in Sunday's play-off final.
Hearts and United will face off against each other in Group A, which also includes East Fife, Stenhousemuir and Cowdenbeath.Hibs will face off against exclusively part-time opposition as they land back in the groups after receiving a bye last season due to their participation in European football. Alloa Athletic, Stirling Albion, Arbroath and Elgin City will have the daunting task of trying to better the Easter Road side.
There's one all-Premiership clash in Group B where St Johnstone and Ross County will be favoured to battle it out for top spot. They're joined by three Angus clubs in Forfar Athletic, Brechin City and Montrose.
Greenock Morton and Queen of the South will provide second-tier tests for 2017 finalists Motherwell, who'll also need to navigate past Dumbarton.
Matchday 1 takes place on the weekend of 13 July, with Matchdays 3 and 5 taking place over the following two weekends.
Matchdays 2 and 4 will take place in midweek, on July 16/17 and July 23/24.
Holders Celtic, along with Rangers, Kilmarnock and Aberdeen, won't enter the competition until the knock-out stages due to their participation in European football.
All eight group winners will advance to the knock-out stages along with the fourth best runner-ups.
The groups in full...
Hearts, Dundee United, East Fife, Stenhousemuir, Cowdenbeath
St Johnstone, Ross County, Forfar Athletic, Brechin City, Montrose
Hibs, Alloa Athletic, Stirling Albion, Arbroath, Elgin City
Dundee, Inverness CT, Raith Rovers, Peterhead, Cove Rangers
Motherwell, Greenock Morton, Queen of the South, Annan Athletic, Dumbarton
Hamilton Academical, Partick Thistle, Airdrieonians, Queen’s Park, Clyde
Livingston, Ayr United, Stranraer, Berwick Rangers, Falkirk
St Mirren, Dunfermline Athletic, Albion Rovers, Edinburgh CIty, East KilbrideREAD MORE - Who finished as the Scottish Premiership's 'dirtiest' team? Here’s where each club ranked in the fair play table