McClaren will replace Nigel Clough, who was sacked after Saturday's defeat to arch-rivals Nottingham Forest.
A statement on the Derby website read: "McClaren, 52, has signed a two-and-half-year deal at Pride Park Stadium and will officially take up his new role at the club on Wednesday, after leaving his position on the coaching staff at Sky Bet Championship leaders Queens Park Rangers.
"He will watch on from the stands for Derby's home game with Ipswich Town on Tuesday evening and will officially take charge of his first match on Saturday (5 October), when the Rams take on Leeds United at Pride Park.
"He will be joined by two other ex-Derby players on what will be a new-look coaching set-up, with Paul Simpson (first-team coach) and Eric Steele (goalkeeping coach) also agreeing to return to the club."
Derby County have confirmed that they also expect to name a new technical director in the near future.
Derby president and 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.
"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."