The 20-year-old, who can play at centre-back or right-back, played at the International Stadium in pre-season as part of the United XI that beat Gateshead 3-0 last month.
After progressing through the ranks at their academy, Williams made thirty-three appearances and thirty-one starts in all competitions for the Magpies` under-23 side last season.
The 6`1” defender netted his first goal for the side against Derby County in October 2015 and was named on the bench for the Premier League victory over West Bromwich Albion the following February.
And, after being critical of his side`s defending at the weekend, Heed boss Neil Aspin will be hoping Williams` addition will provide some extra strength at the back.
Williams is available for selection for tonight`s fixture against Guiseley AFC at the International Stadium.