Rovers will play Newcastle United in the second round of the Carabao Cup.
The tie against Steve Bruce's side is scheduled to take place at St James' Park on either Tuesday 15th September or Wednesday 16th September, with an official date to be confirmed.
The last encounter against the Magpies came in the Emirates FA Cup in January 2019, with the Toon Army earning a victory in the replay at Ewood Park following a 1-1 draw at St James' Park.
The last meeting in the League Cup came back in October 2011, with Gael Givet's dramatic late goal earning Rovers a 4-3 victory on home turf.
Should Rovers make it through to the third round, Tony Mowbray's side will face either Morecambe or Oldham Athletic away from home.
Rovers reached this stage of the compeitition after a 3-2 home victory against Doncaster Rovers at the end of last month, with goals from Lewis Holtby, Joe Rankin-Costello and Adam Armstrong earning cup progress.
The 2020-21 competition has seen a number of significant scheduling changes, with two-legged semi-finals being replaced by a single tie.
The full second round draw can be seen below: