White joins the Blues after the club secured his release from Solihull Moors.
The 22-year-old scored 12 goals in the 2016-17 season for the Moors; their debut season in the National League.
The Birmingham-born attacker had spells in the 2015-16 campaign on loan at both Kidderminster and Boreham Wood from Barnsley.
White becomes Jon McCarthy’s first summer signing.
Welcome to Chester FC, Harry!