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.
To be fair, Steve McClaren is a good manager, i know he didn't do so good at Forest, but they had money to spend, at Middlseborough he didn't have too much to spend and did a good job. When he was England manager i loved him, he tried to change the way we played, he tried to introduce the younger players and move the older players like David Backham on, for sure David could still do a job and has done since McClaren was sacked, but we still haven't won anything, so it's been a waste of time, for me if Steve had carried on with the young England squad he could have actually gone on to achieve something.- dannyjohnson