The 33-year-old has agreed terms with Derby after being released from his contract at Coventry by mutual consent.
Konjic joined Coventry in 1999 when The Sky Blues paid Monaco £2 million for his signature.
"I only worked with Mo for a short space of time but he was clearly a good professional," said Reid.
"I am disappointed to lose a player of his calibre but Mo felt that the time for a move was right.
"I am actively searching for other players at present and I am speaking to numerous clubs about possible signings."
Derby, meanwhile, have announced their retained list and confirmed that goalkeeper Andy Oakes and defender David Walton are free to leave Pride Park - despite both having one-year left on their contracts.
Loan signing Candido Costa has also been told that he can return to Porto, while Spaniard Manel is also leaving the club.
Young defenders Jimmy Turner and Chris Palmer have also been told they can move on, but Kris Weckstrom has been handed a month-to-month deal to prove his fitness.
The club have also confirmed that Adam Bolder and Richard Jackson have both signed new contracts with the club, while talks are progressing with Youl Mawene and Lee Holmes.
