Williams, 25 recently spent three months on loan at Bramall Lane – making his debut in the 3-0 defeat to Huddersfield Town and went onto make a total of 14 appearances for the club.
It is believed that he has penned a two and a half year deal and is likely to make his second debut for the club at Carlisle United on Monday afternoon.
The arrival of Williams will leave Lescinel Jean-Francois, Elian Parrino, Andy Taylor and Marc Warren fighting for the left full-back spot; whilst Matt Lowton can also fill in if required.