The right-back, who has found himself out of favour with the Premier League side of late, is expected to go straight into the Rams' squad for Saturday's visit of Scunthorpe.
Clough, who is celebrating a year in charge at Pride Park, said: "Nicky is a very welcome addition to our squad and we're pleased we have been able to bring him in."
He added: "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 and he also has good experience in both the Championship and also the Premier League.
"We highlighted the need to bring in fresh faces and Nicky fits the bill perfectly for us."
Source: PA
Source: PA