The Rams, managed by former England boss Steve McClaren, will host the Light Blues a week before the SPFL Championship begins.
Ally McCoist's side were due to play in the first round of the League Cup on that day, but this has been been rescheduled because of the Commonwealth Games, as has the Ibrox club's opening Challenge Cup-tie on July 26. No new dates have been decided yet.
Derby narrowly missed out on promotion to the English Premier League having lost the play-off final against QPR at Wembley, and there are a number of familiar names in their squad.
Former Dundee United striker Johnny Russell enjoyed a fine debut season, while fellow-Scots Craig Bryson, Chris Martin, Craig Forsyth and former Kilmarnock striker Connor Sammon are also on their books as is highly-rated English midfielder Will Hughes.
McCoist's side also play pre-season games against Buckie Thistle and Brora Rangers before heading to America and Canada to meet Ventura County Fusion, Sacramento Republic FC, Victoria Highlanders and Ottawa Fury FC in July.
McCoist, speaking on the club website, said: "Derby were very unlucky not to clinch promotion so they will certainly give our boys a tough test.
"Our squad will have featured in six pre-season friendlies before we meet Derby and this match will help us prepare for our Championship campaign."