The veteran defender has found first-team opportunities at Goodison Park limited this season and has moved to Pride Park in the pursuit of regular playing time.
Everton have allowed Stubbs to make the move without a fee being involved and it is a capture that has delighted Rams boss Paul Jewell.
"It's a terrific capture for us. Stubbsy is a first class pro and someone who has been there, seen it and done it," Jewell told the club's official website.
"I'm delighted to have him on board and believe he will add experience and steel to our backline.
"He will train with us on Friday and is very much in contention for a place in the team on Saturday."