Burns, 31, scored 62 goals in 132 appearances for Trafford, including 14 this season.
His previous clubs include FC United, Altrincham, Ashton United and Stalybridge Celtic.
Also stepping up to the first team is striker Sheldon Barrington, who has impressed for the club’s academy in the NPLFA, scoring 15 goals.
Meanwhile, departing the club is winger Shelton Payne. He made 24 appearances for Boro, scoring six goals, including a hat-trick against Irlam in The Manchester Cup.
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