The Rams released a statement confirming Simpson’s impending departure after two years as first team coach at the iPro Stadium.
Simpson’s exit is another part of the reorganisation of the backroom staff at Derby following the appointment of Paul Clement as head coach.
Goalkeeper coach Eric Steele, U21 coach Lee Glover, head of sport science Alessandro Schoenmaker and coach Steve Taylor have already left the club since Clement succeeded Steve McClaren at the beginning of this month.
Rams president and chief executive Sam Rush said: “Paul Simpson leaves Derby County with our thanks for his contribution to the club, both as a player and also on the coaching staff.
“We wish Paul every success for the future in his coaching career.”
Simpson, who played for Derby between 1992 and 1997, will officially depart on July 1. He took up the position of first-team coach in September 2013 following the arrival of McClaren.
Derby said in a brief statement that “announcements relating to new coaching staff appointments will be made in due course.”
McClaren has gradually managed to put together his staff for a new challenge at Newcastle after a lengthy search which saw the club talk to the likes of Phil Neville, Bolo Zenden and Steve Round.
Former Valencia assistant manager Ian Cathro is set to be named as his assistant, while goalkeeping coach Andy Woodman is being lined up for a post at Crystal Palace by former Magpies boss Alan Pardew and potential replacements are being sounded out.
Newcastle are yet to confirm any of the appointments, but are expected to do so in due course.