The Blades have been interested in the 20-year-old for a number of weeks but were forced to wait for him to return to fitness after a hamstring injury.
Riley played 85 minutes of United's 1-0 Premier League 2 victory over Liverpool on Monday.
The full-back has made two first-team appearances for Manchester United.
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League One leaders Sheffield United have signed Manchester United full-back Joe Riley on loan for the rest of the season.