Williams, 26, scored 15 goals from the centre of midfield as the Yellows finished third in the Evo-Stik Premier League before their promotion dream was ended by a play-off semi-final defeat to Grantham.
He now goes to join the league champions to play in National League North, having expressed a desire to play at a higher level.
The Liverpudlian is no stranger to Altrincham, having played for them during the 2014-15 season.
He has also spent time with Colwyn Bay, Halifax, Stockport, Vauxhall Motors, Hyde, Skelmersdale and Telford.
Meanwhile, the Yellows have confirmed their first list of retained players for the 2018/19 season.
Captain James McCarten, league Young Player of the Year Dylan Vassallo, midfielders Gerard Kinsella and Liam Hynes plus defender Adam Carden are all on board.