Williams, 22, has signed a three-year deal after Latics agreed an undisclosed fee with Everton.
Williams leaves Goodison Park after 15 years with the Toffees.
Hailing from Liverpool, Williams has been involved in first-team matchday squads with Everton, having progressed through the academy, though he made his mark during loan spells in the EFL.
In 2017-18, he featured 38 times for Barnsley in the Championship before completing a similar spell with Bolton Wanderers last season, in which he impressed during his 29 appearances.
A tenacious midfielder with good technical ability, Williams’ sole career goal came in spectacular fashion in Barnsley’s 4-2 win at Burton Albion in October 2017.