Shaw had most recently been playing for Chester FC in the National League, and had become a key figure at the club, even having a short spell as caretaker-manager earlier this season.
He made over sixty appearances for Tamworth before departing in 2010, and has since represented the likes of Kidderminster Harriers, Cambridge United, and Alfreton Town.
On the signing, manager Andy Morrell told the club`s official website: "We are really pleased to get such an experienced player in. We wanted to fill the gap left by Ellis Deeney with experience and hunger, and that's exactly what we have done. He will be great for the younger members of the squad, and is sure to lead by example."
Chester chief executive Mark Maguire added: “It has been a pleasure to work with Tom over the last eighteen months. His commitment, drive and enthusiasm for the club, not to mention the respect in which he is held by everyone associated with Chester FC is a credit to him and his family. His willingness to step into the breach earlier this season was the first taste he will have of what I have no doubt will be a long and successful career, I’d like to thank him personally and professionally for all he has done.”
Shaw should be in line to make his second Lambs debut at home to Brackley Town tomorrow.