The 18-year-old midfielder's new terms at Whaddon Road are due to expire in summer 2016.
Williams has made three appearances for Cheltenham so far this season.
The Robins continue their league campaign on Saturday when they travel to Oxford United.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Walsall | 19 | 12 | 4 | 3 | 35 | 19 | 16 | 40 |
| 2 | Port Vale | 20 | 10 | 6 | 4 | 26 | 19 | 7 | 36 |
| 3 | Crewe AlexandraCrewe | 19 | 9 | 7 | 3 | 24 | 16 | 8 | 34 |
| 4 | AFC Wimbledon | 19 | 10 | 3 | 6 | 31 | 16 | 15 | 33 |
| 5 | Doncaster RoversDoncaster | 20 | 9 | 6 | 5 | 28 | 23 | 5 | 33 |
| 6 | Chesterfield | 20 | 8 | 7 | 5 | 35 | 23 | 12 | 31 |
| 7 | Grimsby Town | 20 | 10 | 1 | 9 | 27 | 30 | -3 | 31 |
| 8 | MK Dons | 18 | 9 | 3 | 6 | 30 | 20 | 10 | 30 |
| 9 | Gillingham | 19 | 9 | 2 | 8 | 20 | 16 | 4 | 29 |
| 10 | Bradford CityBradford | 19 | 7 | 7 | 5 | 24 | 19 | 5 | 28 |
| 11 | Notts County | 19 | 7 | 7 | 5 | 25 | 21 | 4 | 28 |
| 12 | Salford City | 19 | 7 | 6 | 6 | 20 | 19 | 1 | 27 |
| 13 | Cheltenham TownCheltenham | 20 | 7 | 5 | 8 | 27 | 28 | -1 | 26 |
| 14 | Bromley | 19 | 5 | 9 | 5 | 23 | 23 | 0 | 24 |
| 15 | BarrowBarrow | 19 | 6 | 5 | 8 | 18 | 18 | 0 | 23 |
| 16 | Newport CountyNewport | 19 | 6 | 5 | 8 | 21 | 28 | -7 | 23 |
| 17 | Fleetwood TownFleetwood | 17 | 5 | 7 | 5 | 23 | 22 | 1 | 22 |
| 18 | Colchester UnitedColchester | 19 | 4 | 10 | 5 | 23 | 22 | 1 | 22 |
| 19 | Tranmere RoversTranmere | 19 | 5 | 6 | 8 | 14 | 26 | -12 | 21 |
| 20 | Harrogate TownHarrogate | 20 | 6 | 3 | 11 | 17 | 30 | -13 | 21 |
| 21 | Accrington StanleyAccrington | 18 | 4 | 6 | 8 | 25 | 33 | -8 | 18 |
| 22 | Swindon TownSwindon | 20 | 3 | 7 | 10 | 23 | 34 | -11 | 16 |
| 23 | Morecambe | 20 | 3 | 5 | 12 | 19 | 36 | -17 | 14 |
| 24 | Carlisle UnitedCarlisle | 19 | 3 | 5 | 11 | 15 | 32 | -17 | 14 |
| > League Two Full Table | |||||||||
