It is understood that Fleck, 22 turned down offers from a number of Championship clubs to sign a three year deal with the S2 club.
He could feature amongst the XI to face Stocksbridge Park Steels today (Kick-Off: 3PM) along with fellow new signings; Mark Duffy, Chris Hussey, James Wilson and Jack O'Connell.
Blades boss Chris Wilder told sufc.co.uk; "John is an outstanding midfield player in League One and we believe he can play at a higher level. He is another to have contract options and we are delighted to get him to Bramall Lane as he is athletic, hungry, a great age and fits the structure of the players we want to represent the club."