"Paul Clement is one of the most in-demand coaches in world football and I am delighted that he has agreed to join Derby County as our new head coach," the club's president and chief executive Sam Rush said.
"He is hugely respected, has exceptional relationships throughout football and tremendous coaching experience at some of the very best clubs in Europe."
Clement began his coaching career with English champions Chelsea and stepped up to the role of assistant when Ancelotti arrived in 2009 before following the Italian to Paris St Germain and then Real for trophy-winning spells.
He steps in for McClaren, who was fired after the club, having led the table for a long stint of the campaign, missed out on the end-of-season promotional playoffs following a woeful collapse.
He becomes the second former Real Madrid assistant to take charge of a Championship club after Aitor Karanka, whose Middlesbrough side lost out to Norwich City in the playoff final last week.
"This is a massive club with fantastic facilities and a superb fan base who deserve success," Clement said
"Having spoken with Sam Rush and the owners I firmly believe we share the same desires and ambitions and that is to once again make Derby County a Premier League club."
Twice English champions Derby were relegated from the top flight in 2008 following a dismal campaign in which they picked up only one win and recorded the lowest Premier League points total of 11.
(Writing by Patrick Johnston in Singapore, editing by Nick Mulvenney)
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