The 24-year-old, who has yet to figure in a first-team game for the Bucks since signing from Altrincham in the summer, completed his move in time to play for the Imps in the New Year's Day derby against Grimsby Town.
Williams broke into the first-team ranks at TNS in 2006 without being able to hold down a regular place and made 11 Welsh Premier appearances for Newtown during a loan spell.
He had a further loan spell at Caersws in 2008/9 and, after completing a total of 34 (+2) appearances for his three clubs, signed for Altrincham,making his Conference debut on the opening day of the 2009/10 season and soon establishing himself as a regular.
Williams' form was recognised by the Wales Under-23 semi-pros and he won three caps.
After two seasons at Moss Lane, he moved to the New Bucks Head but his progress was marred by a pre-season injury and he returned to Altrincham for a three-month spell which has recently ended.