Riley, 20, will spend the rest of the season with the League One side in order to gain some valuable first-team experience.
The midfielder, who can also be employed as a full-back, has tasted first-team action with United, playing twice last season.
His two appearances came in the FA Cup against Shrewsbury and in the Europa League against Midtjylland.
The 20-year-old will be hoping to add to his two senior appearances, as the Blades attempt to win promotion to the Championship from England's third tier.