The 48-year-old's appointment has been confirmed and the former PSV Eindhoven boss is with the Rams squad at their training camp in Florida. He has bagged a four-year contract with the club.
Cocu replaces Frank Lampard, who was installed as Chelsea's new head coach yesterday after just one year in charge at Derby.
Cocu had a highly-successful playing career with PSV and Barcelona, and he played 101 times for Holland.
He won three Eredivisie titles in four years as PSV boss.
Chris van der Weerden is assistant manager and Twan Scheepers is a specialist first-team coach.
Van der Weerden, who is 46, is also a former PSV player and had six years at the club as assistant manager. He has been assistant at Fenerbahce.
Scheepers, who is 47, is a former PSV player and has been an under-21 assistant manager at the Dutch club.
Derby is keen to build on the work of last season when they finished sixth in the Championship and reached the play-off final.
Maintaining the philosophy, style of play and pathway for young players is important are all part of the plan, and they believe Cocu is the ideal choice.
"The style of football is extremely similar to how Frank has been setting Derby up," said chairman Mel Morris. "That is a big part, and I think the ability to embrace youth is something he (Cocu) has a tremendous track record in.
"He has a phenomenal record of achieving success in the Eredivisie.
"We are looking forward to some exciting football and continuing with the philosophy and style of play we saw over the last season."