Burnley's new sporting director Frank McParland hopes to be able to start next season alongside Sean Dyche.
Leeds teenager Alex Purver has agreed a new one-year deal with the club.
Rams manager Steve McClaren believes tying down the Republic of Ireland international could be among the most important pieces of business he will do this summer.
He told the club's official website: "It's fantastic news for the Football Club that Jeff has signed a new long-term contract and it is probably one of the best signings we will make this summer.
"When myself and the coaching staff were appointed last season we were aware that Jeff was a player with plenty of potential.
"Seeing him first hand in training every day and in match situations too, it is very clear he has a lot of qualities.
"He ended last season in very good form and made a real impact on the side, so we'll be looking for exactly the same from him at the start of the new season in August."
Hendrick made 35 appearances last season and scored five times as Derby fell agonisingly short of promotion to the Premier League.