The one-day fixture will be free for spectators who will be able to use the Tom Dollery Members Lounge.
Both counties are set to feature strong sides, with Derbyshire getting the 2019 season underway the following week, at home to Durham in the Specsavers County Championship, starting on Friday 5 April.
Billy Godleman’s side then travel to Gloucestershire for a second four-day fixture, before a block of eight Royal London One-Day Cup fixtures, beginning on Good Friday (19 April).
Head of Cricket Dave Houghton said: “The players are keen to test themselves and get out onto the field for competitive match practice before the season starts.
“We have a talented and competitive squad with a good mix of experience and youth coming through. This fixture, along with further pre-season training, will be a chance to impress and stake a claim for a spot ahead of the opening game against Durham.”
© Cricket World 2019