The 33-year-old has been training with the Rams since leaving former club Accrington Stanley in January.
Speaking of the signing, Derby manager Steve McClaren said: "Lee is an experienced player and we are pleased to have him."
Naylor has made over 500 appearances in his career for sides including Wolverhampton Wanderers, Celtic and Cardiff City.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Leeds UnitedLeeds | 25 | 15 | 7 | 3 | 45 | 16 | 29 | 52 |
| 2 | Burnley | 25 | 13 | 10 | 2 | 30 | 9 | 21 | 49 |
| 3 | Sheffield UnitedSheff Utd | 25 | 15 | 6 | 4 | 34 | 16 | 18 | 49 |
| 4 | Sunderland | 25 | 13 | 8 | 4 | 38 | 22 | 16 | 47 |
| 5 | Middlesbrough | 25 | 11 | 7 | 7 | 42 | 31 | 11 | 40 |
| 6 | West Bromwich AlbionWest Brom | 25 | 9 | 12 | 4 | 31 | 20 | 11 | 39 |
| 7 | Blackburn RoversBlackburn | 24 | 11 | 6 | 7 | 28 | 22 | 6 | 39 |
| 8 | Watford | 24 | 11 | 4 | 9 | 34 | 34 | 0 | 37 |
| 9 | Sheffield WednesdaySheff Weds | 25 | 10 | 6 | 9 | 36 | 38 | -2 | 36 |
| 10 | Bristol City | 25 | 8 | 10 | 7 | 32 | 30 | 2 | 34 |
| 11 | Norwich CityNorwich | 25 | 8 | 9 | 8 | 41 | 36 | 5 | 33 |
| 12 | Swansea CitySwansea | 25 | 9 | 6 | 10 | 29 | 29 | 0 | 33 |
| 13 | Millwall | 24 | 7 | 8 | 9 | 22 | 21 | 1 | 29 |
| 14 | Coventry CityCoventry | 25 | 7 | 8 | 10 | 33 | 35 | -2 | 29 |
| 15 | Preston North EndPreston | 25 | 6 | 11 | 8 | 27 | 33 | -6 | 29 |
| 16 | Queens Park RangersQPR | 25 | 6 | 11 | 8 | 27 | 33 | -6 | 29 |
| 17 | Derby CountyDerby | 25 | 7 | 6 | 12 | 31 | 34 | -3 | 27 |
| 18 | Oxford UnitedOxford Utd | 24 | 7 | 6 | 11 | 27 | 39 | -12 | 27 |
| 19 | Stoke CityStoke | 25 | 6 | 8 | 11 | 24 | 32 | -8 | 26 |
| 20 | Luton TownLuton | 25 | 7 | 4 | 14 | 26 | 42 | -16 | 25 |
| 21 | Portsmouth | 23 | 5 | 8 | 10 | 30 | 40 | -10 | 23 |
| 22 | Hull City | 25 | 5 | 7 | 13 | 22 | 33 | -11 | 22 |
| 23 | Cardiff CityCardiff | 24 | 5 | 7 | 12 | 24 | 39 | -15 | 22 |
| 24 | Plymouth ArgylePlymouth | 24 | 4 | 7 | 13 | 24 | 53 | -29 | 19 |
| > Championship Full Table | |||||||||
