It will be the first time the two sides have met in a decade with the last competitive match also coming in the League Cup back in July 2011 when the Bairns were 4-2 winners at Cliftonhill.
Making up their group is League 2 Edinburgh City and Championship pair Ayr United and Hamilton Accies.
The other four sides in the group will face each other in the opening round of the group stages the weekend before Falkirk face Rovers.
Following that match, they will welcome Hamilton Accies to the Falkirk Stadium on Saturday, July 17, facing off against the North Lanarkshire club for the first time since the 2014 Premiership play-offs.
The Bairns then face back-to-back away trips, first to Edinburgh City on Wednesday, July 21, and then to Ayr United on Saturday, July 24, as they round off their group stage fixtures.
Having been fortunate enough to draw a group with no Premiership sides, Falkirk will fancy their chances of making it to the Last 16 of the competition for the second year in a row.
The eight group winners and three best runners-up will join European qualifiers Rangers, Celtic, Hibernian, Aberdeen and cup holders St Johnstone in the last 16 of the competition.
Meanwhile, Stenhousemuir will also kick off their new season on Tuesday, July 13, with a trip to Dumbarton.
It’s a difficult group for the Warriors who will also face Partick Thistle at home on Saturday, July 17, followed by St Mirren at home on Tuesday, July 20 and Dunfermline Athletic away on Saturday, July 24.
It’s a tricky draw for Stephen Swift’s side who will have to contend with three full-time opponents.
All Saturday matches involving the Bairns and the Warriors will kick off at the traditional time of 3:00pm while the games on Tuesday, July 13 will get underway at 7:45pm.
Edinburgh City v Falkirk on Wednesday, July 21 will also kick of f at 7:45pm while Stenny v St Mirren on Tuesday, July 20 will get underway slightly earlier at 7:30pm.
The second round of the competition is due to be played on the weekend of August 14 and 15.