Huddlestone started his career with the Rams and returned in 2017 after a lengthy spell at Tottenham and four seasons with Hull.
The 33-year-old, who has made 12 appearances this campaign, was in talks with Derby about remaining at Pride Park longer-term, as a statement from the club said, but no agreement was seemingly reached.
The midfielder said on Twitter: "My contract has now expired so it's likely to be a new chapter for myself, which is exciting times as I still feel I have a lot to offer on and off the field.
"Our objective was to gain promotion, during my three years we haven't quite been able to get over the line. A bit more luck along the way and who knows what could have been.
"The lads are in a fantastic position at the moment and have everything to play for in the remaining games to surprise a few people.
The former Enlgand international was an unused substitute during the Rams 2-1 home win over Reading in the Championship on Saturday and after making more than 150 appearances for Derby, Huddlestone hopes to reunite with the club later down the line.
He added: "There is too many people to thank from the club on here but know your hard work and efforts was always thoroughly appreciated by me and the lads.
"Good luck for the future Rams, I'll be watching as a fan hoping the lads can finish off a special if not very weird season on many levels. I'm sure our paths will cross once again in the future."