An offer, effectively lodged at the eleventh hour, was accepted by the Blades on transfer deadline day (31st August). The fee the Blades will receive is £1.1million + add ons.
The deal was agreed between the two clubs on Wednesday night but it needed rubber-stamping by the relevant authorities, and it now has done.
Slew penned a new two-year contract with the Blades in July, but Rovers' offer was too good to turn down as far as the club and the player himself are concerned.
Blades director Scott McCabe said: "It was an attractive offer and one we were unable to refuse for what is, essentially, an unproven player."
Manager Danny Wilson also had his say on Slew's departure: "I don't think it is a good move for his career, I think he should have stayed with us to develop and I have always said that publicly. In my opinion his progression would have been best here but it is down to the player and agent, so we move on to the next chapter
"We wish him all the best because we know he is moving to a very good football club in Blackburn Rovers.
"I wasn't involved in the negotiations, but the offer was tweaked and tweaked until the clubs reached an agreement and that is what happened in the end."
The 18-year-old was instrumental in United's progression into the FA Youth Cup Final.
Slew joins the Ewood Park outfit on a four-year-deal.
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