The experienced McClaren, who had been working as first-team coach under Harry Redknapp at Queens Park Rangers, signed a two-and-a-half-year contract with Derby who are 14th in the table with 11 points from nine games.
Saturday's 1-0 loss to Nottingham Forest was enough to earn Clough, 47, the sack following a series of poor home performances.
"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," Derby chief executive Sam Rush said on the club website (www.dcfc.co.uk).
McClaren will hope he can reverse County's fortunes whilst dispelling any lingering memories of underwhelming periods in charge of Forest and the England national team.
The former Middlesbrough boss guided Dutch club FC Twente to their first Eredivisie title in 2010, but is still best known for overseeing England's disappointing exit from the 2008 European championship qualifying group after defeats by Russia and Croatia.
It will be McClaren's third spell at Derby, having played for the club between 1985 and 1988 as well as working as assistant manager under Jim Smith and winning promotion to the Premier League in 1996.
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- Queens Park Rangers
- Harry Redknapp