The Manchester-born frontman joins on a three-month deal having enjoyed spells in the National League with York City, Southport and Gateshead last season.
Wright, who turns 21 next week, made his Town debut on Tuesday night as a half-time substitute against Salford City and will be involved for Saturday’s trip to AFC Telford United.
Prior to last season Wright was a regular in the Blades’ under-21 set-up, as well as turning out for then-Evo-Stik League Premier side Ilkeston FC and Toolstation Northern Counties East League outfit Hallam FC on loan deals.
During his time with Hallam, Wright netted 14 times in just seven appearances, scoring in every game he played.
Wright is described by the Blades as a strong and uncompromising forward with an eye for goal.
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