The 18-year-old arrives on a two-year deal with the option of a third and will add to the competition for places in the Blades' back line.
McGahey made his senior debut for the Seasiders against Burnley in April, impressing with his composure. He went on to make a total of four appearances last season, but Blackpool’s off-field issues alerted Blades manager Nigel Clough to his availability.
The two teams were unable to agree terms and the fee will be set by tribunal.
Clough said: "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. He will admit that he is not the finished article but we are delighted that he has chosen to join us to aid his development.
"Harrison is a big strong defender and there are a number of similar characters at Bramall Lane, from whom he can learn his trade."
He is United's ninth signing of the summer and the second this week following the capture of fellow defender Craig Alcock and joins former Blackpool players Chris Basham and Bob Harris, who are already at Bramall Lane.
Such was the potential of McGahey at Blackpool that former manager Barry Ferguson urged the hierarchy at Bloomfield Road to tie him down to a long-term contract.
He said at the time: “Blackpool have one hell of a player on their hands and they need to get him sorted out, otherwise they'll miss out on a top player.”