Williams scored the winning try against Gloucester in the Cup

The 23-year-old returned to the club in December as injury cover after a season and a half in Wales with the Ospreys.

"I regard the club as home and I am delighted to be signing a new deal," said Williams. "I feel in a position to develop and improve my game.

"My immediate goal is to enjoy my rugby and look to secure my place. Next season I hope to be able to challenge the established scrum halves."

Williams has been used as an emergency three-quarter by Bath and scored the winning try from the wing in this month's Powergen Cup semi-final against Gloucester.

He lost his place at the Ospreys when the Neath-Swansea side recruited New Zealander Jason Spice from Wellington last summer.