Sestanovich, 21 had been offered a contract by County after impressing boss Charlton Palmer in the reserves.
But Blades boss Neil Warnock has also been tracking the ex-Manchester City ace, who has signed a two-year deal from Ryman Premier League club Hammond and Richmond.
"He is a raw, promising player with a good physique and hopefully, with a bit of coaching, he could be an asset," Warnock told United's website.