Winger Yannick Bolasie has signed a new three-year contract at Crystal Palace.
Bayern Munich have announced that Spanish midfielder Xabi Alonso has joined the club from Real Madrid.
The former England boss 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."
Derby plan to appoint a technical director in the near future to work alongside McClaren, who will watch the Rams' home Championship fixture against Ipswich tomorrow from the stands.
Academy manager Darren Wassall will take charge of first-team affairs for that match, but McClaren will be at the helm when Leeds visit Pride Park on Saturday.
McClaren's reputation in this country suffered significant damage thanks to his ill-fated spell in charge of England, but he is still revered by many Derby supporters for his achievements alongside Smith.
The former Rams midfielder of the mid-late 1980s was part of Manchester United's treble-winning staff in 1999 and also enjoyed success as a manager in his own right with Middlesbrough and FC Twente.
McClaren won the 2004 League Cup with the Teessiders - still the club's only trophy in its history - and two years later guided Boro to the UEFA Cup final where they lost 4-0 to Spanish side Sevilla.
In 2010 FC Twente were crowned Dutch champions for the first time in their history.
His last managerial role in English football was at Forest, but he lasted just 111 days before resigning following a fall-out with the club's board over a lack of financial backing.
A short stint at German side Wolfsburg and an unsuccessful return to Twente sandwiched McClaren's time at the City Ground.