The 30-year-old Republic of Ireland international last night signed a four-year deal at the Stadium of Light for an undisclosed fee - understood to be in the region of £5million - to end his long association with the Red Devils.
O'Shea told SAFC TV: "It was one of those things. I was there for 13 years and they were 13 fantastic years.
"But this is a nice new exciting chapter for me now and hopefully we can have good times with Sunderland like I had at Manchester United.
"When I spoke to Steve, the manager, and heard his ideas and the ambition he has shown this summer in the players he is signing and the improvements he wants to make at the club and the strides he wants to make to go forward, I am just looking forward to being a part of it now."
O'Shea signed for the Black Cats just hours after former United team-mate Wes Brown, 31, had put pen to paper on a contract of the same length, again for an undisclosed fee thought to amount to £1million.
Sunderland made a joint bid of more than £12million for the pair and midfielder Darron Gibson last month, although it has taken some time to push home their interest.
In O'Shea's case, however, that was not indicative of any indecision on his part.
He said: "Once I heard reports about the club and the people here, the ambitions and what the manager is all about, it was the only place I was going to come to once I knew the deal was on the table and close to being done.
"I had to wait a few weeks for the birth of my child - that's why it seems protracted, but it wasn't really, it was fairly straightforward, and I am delighted that it's all been done now."
O'Shea and Brown both boast a glittering array of winners' medals from their time at Old Trafford, but they join the Black Cats as Bruce attempts to make a push towards the upper reaches of the Premier League.
The Irishman, the manager's eighth summer signing to date, said: "I am coming to Sunderland now after one of their most successful seasons in the Premier League, and always the aim with every team is to improve on the season before.
"That's what, I am sure, the manager will be drilling into us in pre-season, that we want to improve on the season before, and if we can do that, I'm sure the club and the fans will be delighted."
Bruce is hoping to land his ninth new acquisition on Friday with Blackpool midfielder David Vaughan understood to have travelled to Wearside yesterday with a view to completing a free transfer move.