The former England boss - who had been linked with the vacant Sunderland job - was the Rams' first choice to succeed Nigel Clough.
Clough was sacked on Saturday evening just hours after Derby's 1-0 defeat to east midlands rivals Nottingham Forest at the City Ground, ending his four-and-a-half-year reign.
McClaren arrives from Sky Bet Championship rivals QPR, where he has been a coach under Harry Redknapp since the beginning of July.
No compensation was necessary as the short-term deal he signed in the summer was set to expire this week.
The 52-year-old's appointment sees him return for a third spell at the club he served first as a player and then assistant to Jim Smith, whom he helped to guide Derby to the Premier League in the 1995/96 season.
He will have former Carlisle and Preston boss Paul Simpson as first-team coach and Eric Steele, formerly of Manchester United, as goalkeeping coach.
Derby chief executive Sam Rush said: "We are thrilled to announce Steve McClaren as our new head coach as well as Paul Simpson and Eric Steele in their respective roles.
"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.
"He also has a network of contacts both on a European and global scale, and has also proved in the past that he can identify talent and develop it on the training ground, especially younger players, which is where our Academy comes into play and his working relationship with Darren Wassall is critical to our on-going success.
It is also important that Steve, Paul and Eric know what it means to play for Derby County and they have been at the club during the good times.
"Steve was a driving force behind the club's promotion under Jim Smith in the 1990s and you only have to look at his CV to discover what a hugely talented coach he is.
"We are very much looking forward to letting Steve get on with the job in hand and helping Derby County move in the right direction."