Williams scored 14 goals last season for Belper as well as making his 100th appearance in a Nailers shirt.
The midfielder thanked everyone involved with the club for the way that they have helped him ahead of this exciting move for him.
Williams said: “I would like to thank everyone involved in the club behind the scenes and wish everyone the best for the future.
“I am really excited about signing for Gainsborough and I am looking forward to kicking on and trying to improve myself.
“It is important now that I don't get comfortable and think the work is done, I must now kick on again and improve myself.
“It was difficult to leave Belper, I have a great relationship with everyone there, especially the players and the manager Charlie, the move seemed to tick all the boxes which is why I went ahead with it.”
Williams added that he was excited for the future for the Nailers and believes that they could make a promotion chase this season.
He said: “I hope the club goes onto better things this season, most people know what that bunch of players from last season are capable.
“The thing we missed was consistency, if they can add that to their game, I think Charlie will have them fighting for the playoffs.”
Williams’ new club managed to secure survival on the final day of the season, condemning Worcester to relegation.
Gainsborough will face some big clubs in the National League North, many of which having previously played in the football league.
Facing these big clubs is an opportunity that Williams himself is relishing as he said: “my aim is to play as high as possible, and the thought of playing in the conference north, against sides like Salford and Stockport would have been very hard to turn down.”
Williams will join up with former Spalding United boss Dave Frecklington in his new role and everyone at Belper Town wishes him the best.