The 20-year-old moves to Bramall Lane for £3million and becomes Blackwell's seventh signing of the summer.
Blackburn Rovers winger Keith Treacy also joined the Blades on a long-term loan deal while former Hull City player Ryan France has penned a two-year contract with the club.
The Cardiff City striker Ross McCormack has handed in a transfer request, amid rumours of interest from several Premier League clubs.
The Scotland international, 22, signed a new long-term contract with the Bluebirds only a matter of weeks ago, having scored 23 goals in his first season in south Wales.
Chairman Peter Ridsdale told the club's official website: "Ross McCormack telephoned me to indicate that if another club came in for him, he would wish to leave.
"This is three weeks after signing a new four-year contract. I told Ross that we had not had any bids for his services and unless he knew of interest that we were unaware of, then he would remain a Cardiff City player.
"I wish to make it clear that if this is a method for any other club to believe that Ross would be allowed to leave Cardiff City 'on the cheap', that this will not be the case."
The Ipswich Town manager Roy Keane has supplemented his squad with the purchase of Colin Healy.
The midfielder, 29, who moves to Portman Road from Cork City for an undisclosed transfer fee, has penned a two-year contract with Town.
Peterborough United have continued their summer recruitment with the acquisition of 18-year-old striker
Doncaster Rovers have handed trials to former Premier League players Quinton Fortune and John Oster.
The Rovers defender Jos van Nieuwstadt must have surgery on a groin injury, meaning he is unlikely to be fit for the start of the season.