"Nicky can play at right-back or centre-half so it is nice to have someone available to us who is equally comfortable in either position."
Hunt, 26, fell out of favour under former Bolton manager Gary Megson and has not played this season.
Clough added: "He also has good experience in both the Championship and also the Premier League.
I was a fan of his when he was a Bolton regular. Is there any reason why he has dropped out of your first team? Randomero "We highlighted the need to bring in fresh faces and Nicky fits the ball perfectly for us."
Derby needed a right-sided defender as injuries and the end of Freddie Stoor's loan spell from Fulham have left the Rams short of defensive cover.
Hunt is expected to go straight into the squad for Saturday's home game against Scunthorpe United.