Clough, whose late father Brian took the club from the old Second Division to become champions of England and European Cup semi-finalists during his spell in charge between 1967 and 1973, had been heavily tipped to succeed Paul Jewell who resigned last week.
The former Liverpool, Manchester City and Nottingham Forest striker, 42, makes the step into league management for the first time following a decade in charge of non-league Burton Albion.
And Clough’s exit could be good news for Wrexham – Burton are currently running away with the Blue Square Premier as they are 13 points clear in the sole automatic promotion spot and are on course to make the step up to the Football League for the first time in their history.
Burton are 20 points ahead of seventh-placed Wrexham, although they have played four more games than Dean Saunders’ side.
Dragons fans will also be relieved to see Clough confirmed as the new Rams manager after Saunders was linked with the job at Pride Park.
Brian Clough was football‘s most celebrated maverick manager. He joined Derby in 1967 from Hartlepool and, a year later, the Rams were promoted to the old First Division.
They won the title in 1972 and reached the semi-finals of the European Cup the following year, beaten by Juventus amid uproar over allegations of match-fixing.
In spite of Clough’s departure from the club after a row with the board – and subsequent success with fierce rivals Nottingham Forest – he remained a hero to Derby fans.
With caretaker manager Chris Hutchings having departed, academy manager David Lowe takes charge of the team for tonight’s game.