Tudor and Tann, both 27, have been training with the club since Saturday and both played a part as the Stutes kicked off their pre-season campaign with a 2-0 win over Dereham Town.
With Patrick Ada and Mat Mitchel-King having left the club, Histon were in the market for an extra defender and Tann is looking forward to playing alongside Stutes stalwart Matt Langston in the back four.