McGahey, 18 joins the Blades after playing just a handful of games for the Tangerines but a fee will be involved following a tribunal havin g being initially from their Academy squad.
Blades boss Nigel Clough told sufc.co.uk; A number of the coaching staff watched Harrison at the end of last season and he has potential, that's what we see in him."
Meanwhile Championship outfit Brighton & Hove Albion have completed the signing of Barnsley striker Chris O'Grady, ending speculation of a move to Bramall Lane.