Williams joined The Hatters on trial late last month from non-league Hednesford Town and the right back has impressed the former Macclesfield Town and Northern Ireland boss with his abilities.
He had earned a trial with Division Two rivals Oldham Athletic last season but Hednesford rejected the bid Latics boss Iain Dowie made for Williams back in January.
McIlroy revealed that the move will be completed next week and that the defender will stay for the rest of the season.
"He'll join us on a free transfer from Hednesford until the end of the season," McIlroy told the club's official website.
"Everything should be done by Monday."
Meanwhile, central defender Rob Jones has extended his loan with Macclesfield Town, despite being sidelined until the New Year following surgery on an injured knee.
