United have paid an undisclosed, club-record fee for a 25-year-old defender with proven leadership qualities and Championship experience.
Brentford captain John Egan has penned a four-year-deal at Bramall Lane, to become Chris Wilder's second quality summer addition, after the arrival of Manchester United stopper Dean Henderson.
Twice-capped Republic of Ireland international Egan has made 67 appearances for the Bees during the last two seasons and is regarded as one of the most consistent defenders in the Championship.
Egan, who began his career at Sunderland, is no stranger to Bramall Lane, having played once for the Blades during a short loan spell in the second half of the 2011/12 campaign under Danny Wilson. Prior to his time at Griffin Park, the central defender amassed nearly 100 appearances as he impressed at Gillingham.
Boss Chris Wilder is delighted the Cork-born man sees his long-term future at Bramall Lane and believes the Blades have got a great deal.
The gaffer remarked: "John has been our number one target in that position throughout the summer, it has been going on a while and we've kept it close to our chests because we've had to. I've monitored him for a number of seasons now and he is a defender who defends properly and he's been excellent as skipper for Brentford.
"We see him as a leader and he is worthy of the fee we've paid for him, in my opinion he is a better player than a couple of those who have already moved for bigger fees this summer. His Championship experience will be crucial as is his experience of being at the right end of the division.
"He's a great age, will develop with us and when that happens I have every confidence that he will be a regular international with the Republic of Ireland."