Short, who played for Rovers from 1999-2005, will take up a position as a member of the first-team coaching staff at Ewood Park with immediate effect.
The two Championship clubs - who meet at Pride Park in their opening game of the 2013/14 season - have agreed a compensation package for the 44-year-old, who was once the Rams' record signing, joining from Notts County for £2.65m in 1992.
He played 143 games for the Pride Park club and had spells at Everton, Sheffield United and Scarborough. He has also managed Hungarian side Ferencvaros and Notts County.
Appointed in September 2011, Short was charged with identifying players aged 13-16.
He will now link up with Rovers first-team boss Gary Bowyer, an ex-Derby academy coach.
Rams boss Nigel Clough told club's website: "Craig has played an important role in the recruitment of our Academy prospects during his time at the club.
"I would like to thank him personally for his contribution and wish him all the best for the future."