The 19-year-old has signed a one-year deal with the Alex after impressing during the term of his first professional contract.
White enjoyed a number of loan spells last season but will be targeting a place in the first team when they return for pre-season in July.
The Chester-born full-back follows in the footsteps of Harry Clayton and Paris Bateman who both recently pledged their immediate futures to the Railwaymen.
