Freeman, 27, has become the club’s first summer arrival since winning promotion back to the Premier League.
He has signed a three-year deal, with the fee reportedly being a club record of around £5m, according to national reports.
It eclipses the record £4m that the Blades paid out to Brentford to sign John Egan last summer.
Helder Costa has set his sights on helping Leeds United reach the Premier League with Marcelo Bielsa this season after his move from Wolves was sealed yesterday afternoon.
Costa, 25, became United’s fourth summer signing following his arrival at Elland Road on an initial one-year loan deal. The winger will make the switch permanent next summer for an undisclosed fee, having already agreed a four-year contract with the Whites until 2024.
The Portuguese forward said: “It is almost the same squad as last season here, the quality is there and, hopefully, we can push even further and get promoted this season.”
Meanwhile, Whites centre-half Aapo Halme, 21, has joined Barnsley for an undisclosed six-figure fee – becoming the Reds’ second defensive signing in less than 24 hours after the capture of AFC Wimbledon’s Toby Sibbick.
Halme, who will help fill the void following the £3m sale of Ethan Pinnock to Brentford, has signed a three-year deal with the option of a further year.
Rotherham United have completed the signing of Newcastle United midfielder Dan Barlaser, 22, on a season-long loan.
Barlaser is the Millers’ fifth newcomer of the summer following the earlier additions of £400,000 striker Freddie Ladapo, midfielder Shaun MacDonald, French winger Julien Lamy and forward Carlton Morris.