The 25-year-old, the captain at Griffin Park last season, has signed a four-year deal to become the Blades’ second capture of the summer.
His fee beats the previous club record, set when James Beattie arrived for around £3.5m shortly after relegation from the Premier League in 2007. Egan has been wanted by manager Chris Wilder for the best part of 18 months and it is understood a number of offers have been rebuffed by the Londoners during that time before the player making it clear he wanted to move broke the deadlock.
“John has been our number one target in that position throughout the summer,” said the United chief.
“It has been going on a while and we have kept it close to our chests because we have had to. I have monitored him for a number of seasons now and he is a defender who defends properly and he has been excellent as skipper for Brentford.
“We see him as a leader and he is worthy of the fee we have 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 is 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.”
Egan’s arrival comes amid speculation on the south coast of a likely bid from Brighton & Hove Albion for United defender Jack O’Connell.
The Liverpudlian was an ever-present last term as the Blades made an impressive return to the Championship. Sources in Brighton have confirmed the Premier League club’s interest is genuine.
As for Egan, this represents his second move to Bramall Lane. He had a short loan spell with the Yorkshire club in 2012 under Danny Wilson but made just one appearance in a 3-2 defeat at Walsall. The Irishman had a loan spell at Bradford City the following season but it took a free transfer move from Sunderland to Gillingham in 2014 to get his career up and running.