The 21-year-old joins the League Two side in a permanent move for an undisclosed fee.
Halliday has enjoyed successful loan spells at Hartlepool and York, and came within a whisker of helping Accrington Stanley to promotion last term, where he played 35 times during a season which saw the Lancashire club reach the League Two Play-Offs.
The right-back, who joined Boro's Academy from his hometown club Redcar Town in 2010, featured with Aitor Karanka's senior squad during pre-season and also joined the summer training camp in Marbella.
Everyone at MFC wishes Brad all the best for the future.
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