The 42-year-old - who played for his father at Nottingham Forest - left Burton Albion after a 10 year spell there to take over the Championship strugglers, though, he won't be in the dugout for Wednesday's League Cup semi-final first leg match against Manchester United.
"This is a fantastic opportunity for me and one that I relish," said Clough, who has impressed at Burton and leaves them top of their division the Blue Square Premier with a 13 points advantage over their nearest rivals.
"I know the club inside out. It has always had a special place in mine and my family's heart (he was six when his father guided the previously unglamorous side to the then First Division now Premiership title) and I know that this is one of the most exciting jobs in football.
"Derby County has everything - tremendous support, a first-class stadium, magnificent training facilities and an ambitious ownership group looking to grow the club even further. Also, we have a terrific squad of players already here and I can't wait to start working with them."
Derby have been without a manager since Paul Jewell left on December 28 after the former Bradford and Wigan handler had failed to revive their fortunes both in keeping them in the Premiership and then seeing them going into freefall in The Championship.
Derby chairman Adam Pearson told BBC Radio they had got the right man for the job in hand - 'The Rams' are presently five points above the Championship relegation zone. "We are delighted to have Nigel on board. He is right man for this club at this time, he has created a fine legacy at Burton and wants to do exactly the same at Derby. He sees it very much as a long-term project.
"There was no sentiment or romance involved in the appointment, you can't have that in football. He's tough enough to take the club forward in his own style."
Jewell's assistant Chris Hutchings had been in temporary charge of Derby, but he has left the club so academy manager David Lowe will be in charge for the League Cup semi-final first leg.