The 35-year-old joined them on loan from Scunthorpe in February and has now agreed a 12-month deal to stay on with the Lambs.
Johnson made 19 appearances for United, scoring three times.
His last appearance for the Iron came in the home match against Swansea City on February 18.
However at that time Tamworth were interested and, with no guarantee of first team football, it was agreed that the former Aston Villa and Celtic man could make the move.
United announced last week that Johnson was being released.