The 30-year-old Republic of Ireland international travelled to Wearside for a medical this morning and wasted little time in becoming Steve Bruce's eighth summer signing.
Like Brown, he has joined for an undisclosed fee after United last month accepted a joint offer of more than £12million for the pair and midfielder Darron Gibson.
O'Shea said: "Once I'd heard reports about the club and the people here, the ambitions and what the manager was all about, it was the only place I was going to come to."
Manager Steve Bruce added: "John has been a solid, consistent part of Manchester United's squad for well over a decade, which goes to show the fantastic pedigree of player we have signed.
"He is a wonderful professional both on and off the field and his wealth of experience and versatility will be great attributes for us.
"I'm delighted with the players we have been able to secure ahead of the new season."
O'Shea boasts five Barclays Premier League titles, an FA Cup winners' medal, three League Cup successes and a Champions League triumph among his list of achievements at Old Trafford.
He is also a stalwart of Giovanni Trapattoni's Ireland team and like Brown, will bring experience and a winning mentality to the Stadium of Light.
He made almost 400 appearances for the Red Devils during his 12 years with the club and it was initially thought he would take some persuading to leave.
However, despite having to delay talks earlier this week as his wife gave birth, he managed to tie up his move swiftly today.
Meanwhile, the Black Cats were tonight also closing in on a free transfer move for Blackpool midfielder David Vaughan, who is understood to have travelled across the Pennines earlier today with the intention of sealing his own switch.
In a busy day for the Wearside club, legal director Margaret Byrne was appointed new chief executive and Bryan "Pop" Robson returned as chief scout.
