The 33-year-old has been training with the Rams after leaving League Two side Accrington Stanley in January.
Rams head coach Steve McClaren said: "Lee is an experienced player and we are pleased to have him."
Former England Under-21 international Naylor played over 300 games for Wolves and has made more than 500 career appearances in total.
Derby County have signed experienced former Wolves and Celtic left-back Lee Naylor until the end of the season.