"I am absolutely buzzing," he told the club's website. "This is a fresh start for me. After not playing too regularly over the last two seasons I'm really eager to come here and make an impact."
Hendrie's first game for the Rams could be against his old club next Saturday, and the 32 year-old is hoping to make a big impact at Pride Park.
"It's crazy really that my first game will be against United," he said.
"It would be fantastic to be involved and to score the winner. That would be a dream come true."