The Republic of International has been a free agent since coming off contract at the end of last season.
Hendrick spent last season on-loan with Sheffield Wednesday. He has signed a contract to the end of the campaign with the Rams.
"Obviously, Jeff knows the club inside out, he was here when I was playing as well, so I know the kind of character he is," Derby manager John Eustace told BBC Radio Derby.
"I think he'll help the dressing room from now until the end of the season. He's a very fit, athletic lad, looks no different now to when I was playing with him, and has had a fantastic career."
Hendrick told the Derby website: "I turned some things down over the summer and January, they just didn't feel right to me, didn't excite me.
"I'm not fully fit. You can't be unless you're training and playing games but the main thing was getting in amongst the group and getting sharper."
Hendrick added: "I'm an older player now, so maybe I can bring a bit of experience to help players in any way I can. If I didn't think I could bring something, there'd be no point in me coming here and being away from my family."