The 29-year old has moved to Cantilever Park after completing a successful one-month loan stint. He made more than 100 appearances for Altrincham across two spells.
He scored 15 goals in 72 appearances for the Yellows between 2016 and 2018, before moving up to National League North.
In 2017/18, Williams finished second top scorer to help the Yellows finish third in the Northern Premier League.
He has scored one goal in seven league appearances for Paul Carden's side so far this season.
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