McClaren has agreed a two-and-a-half-year deal with the Championship outfit that sees him return to Pride Park 14 years after leaving to join Manchester United as Alex Ferguson's assistant.
In his previous spell at the club, McClaren assisted Jim Smith as they won promotion to the Premier League.
|14/1||Derby are 14/1 with BetVictor to win promotion from the Championship
After his two-year-spell at Old Trafford, McClaren went on to manage Middlesbrough, Twente, Wolfsburg, Nottingham Forest and England.
The 52-year-old arrives at the club after Clough was sacked following their 1-0 defeat to fierce rivals Forest at the City Ground on Saturday.
Clough had spent over four years at the club but was not deemed able to take them to the next level by the owners.
"We are thrilled to announce Steve McClaren as our new head coach," Derby president and chief executive Sam Rush told the club's official website.
"When we announced the departure of Nigel Clough it was stated that we were conducting a comprehensive review of the football structure, and we believe this is a major step forward in that regard.
"Our goal is to have Derby County competing for a play-off place and beyond, and we feel with Steve and his team at the helm we have a great opportunity to do so.
"Steve is a highly qualified coach with all the skill-sets required to be a success here at Pride Park."