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 | Port Vale | 15 | 9 | 3 | 3 | 23 | 16 | 7 | 30 |
| 2 | Walsall | 14 | 8 | 3 | 3 | 27 | 15 | 12 | 27 |
| 3 | Notts County | 15 | 7 | 6 | 2 | 23 | 13 | 10 | 27 |
| 4 | Doncaster RoversDoncaster | 15 | 8 | 3 | 4 | 21 | 17 | 4 | 27 |
| 5 | Crewe AlexandraCrewe | 14 | 7 | 4 | 3 | 17 | 13 | 4 | 25 |
| 6 | MK Dons | 15 | 7 | 3 | 5 | 24 | 17 | 7 | 24 |
| 7 | Grimsby Town | 15 | 8 | 0 | 7 | 19 | 25 | -6 | 24 |
| 8 | Gillingham | 15 | 7 | 2 | 6 | 16 | 12 | 4 | 23 |
| 9 | Chesterfield | 15 | 5 | 7 | 3 | 28 | 18 | 10 | 22 |
| 10 | Bradford CityBradford | 15 | 6 | 4 | 5 | 20 | 16 | 4 | 22 |
| 11 | BarrowBarrow | 15 | 6 | 4 | 5 | 16 | 12 | 4 | 22 |
| 12 | Fleetwood TownFleetwood | 14 | 5 | 6 | 3 | 20 | 15 | 5 | 21 |
| 13 | Salford City | 15 | 5 | 5 | 5 | 14 | 17 | -3 | 20 |
| 14 | AFC Wimbledon | 12 | 6 | 1 | 5 | 18 | 10 | 8 | 19 |
| 15 | Newport CountyNewport | 15 | 6 | 1 | 8 | 19 | 26 | -7 | 19 |
| 16 | Cheltenham TownCheltenham | 15 | 5 | 3 | 7 | 19 | 22 | -3 | 18 |
| 17 | Tranmere RoversTranmere | 14 | 4 | 5 | 5 | 10 | 17 | -7 | 17 |
| 18 | Accrington StanleyAccrington | 14 | 4 | 4 | 6 | 18 | 22 | -4 | 16 |
| 19 | Bromley | 14 | 3 | 6 | 5 | 16 | 18 | -2 | 15 |
| 20 | Harrogate TownHarrogate | 15 | 4 | 3 | 8 | 12 | 21 | -9 | 15 |
| 21 | Colchester UnitedColchester | 14 | 2 | 7 | 5 | 17 | 21 | -4 | 13 |
| 22 | Swindon TownSwindon | 15 | 2 | 6 | 7 | 16 | 23 | -7 | 12 |
| 23 | Carlisle UnitedCarlisle | 15 | 3 | 2 | 10 | 13 | 28 | -15 | 11 |
| 24 | Morecambe | 15 | 2 | 4 | 9 | 14 | 26 | -12 | 10 |
| > League Two Full Table | |||||||||
