Simpson, who played for the Rams between 1992 and 1997, has said that he is glad to be back at the East Midlands outfit.
"I got a call from Steve at 8.30pm last Sunday night to say he was coming in," Simpson told the Derby Telegraph.
"My only question was 'when do we start?' I am absolutely thrilled to be back at the club. I loved every minute of my time here as a player and you always have aspirations to come back in some capacity.
"It is good to come to somewhere with so many positive memories. What we have to try to do now is create new memories. We want to get the place buzzing."
McClaren's first match in charge of Derby will be against Leeds United on Saturday.