The 26-year old fell out of favour under Gary Megson and decided to try his luck away from the Reebok Stadium despite the fact Megson was sacked recently.
Rams boss Nigel Clough said Hunt's signing was a great asset to his squad as he strives to shake things up.
"Nicky is a very welcome addition to our squad and we're pleased we have been able to bring him in," he said.
"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."