Davies was due to become a free agent at the end of the season, but after a campaign in which he scored five goals in 26 appearances, boss Nigel Clough was keen for him to stay.
The 31-year-old joined the Rams from League 1 side Notts County during the January 2011 transfer window for an undisclosed fee.
Clough said: "We are pleased Ben is going to be sticking around for another year. He's been an important player for us, especially in the second half of the season when we've started with him and when he's come off the bench in games.
"Ben understands he might not be starting single every week, but he appreciates how highly we value him and knows he can still have an impact on the side.
"On numerous occasions this season, we've seen Ben's versatility; he's played right across midfield and also in both full-back positions as well, so if there's an emergency we know he's capable of doing that job.
"He never moaned about it either, he just got on with his job and that's what we like about him. We didn't involve him early in the season but that wasn't anything against him. But what Ben did was keep his head down and work his way back into the side.
"He is a fit lad so there are no doubts on that front, his attitude is exemplary and he's a great player to have around the place."