The 26 year old moves to join former Rams boss John Gregory on a 2.5 year deal. Gregory has said the signing of Bolder is a "significant coup" for the club.
Bolder leaves the Rams after nearly seven years with the club, joining the Rams on the 27th March 2000. He played 115 times for the Rams and scored eleven goals.
The departure may not be the last of the current transfers during the January window. The Rams have stocked up with mainly midfield talent and it came as no surprise to lose Bolder.