The Magpies agreed a deal with United on Thursday afternoon and Cofie was at Meadow Lane on Friday morning to complete his move, after meeting with caretaker manager Chris Kiwomya.
Cofie, who was snapped up by Sir Alex Ferguson after impressing for Burnley as a youngster, spent the first part of this season on loan at the Magpies' npower League One rivals Sheffield United, making eight league starts and scoring two goals for the Blades.
The 20-year-old made 18 appearances for the Yorkshire club before returning to Old Trafford in January.
Cofie could go straight into Kiwomya's squad for the league game at home to Crewe on Saturday.
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