The 33-year-old was a free agent after his contract with Sky Bet League Two club Accrington was cancelled by mutual consent.
He has spent the last month training with the Rams and has appeared for the U21 side in their matches against Sheffield Wednesday and Crewe.
Naylor started his career at Wolves, where he worked under academy manager Chris Evans, who is now head of football operations at Derby, and made almost 300 league appearances for Wanderers before joining Celtic in 2006.
He made 100 league appearances for the Glasgow club and then moved to Cardiff in 2010. He joined Accrington at the beginning of this season.
Naylor will provide cover for Derby's regular left-back Craig Forsyth for the rest of the campaign.
Derby boss Steve McClaren told the club's official website: "Lee is an experienced player and we're pleased to have him on board for the rest of the season."