Bruce has left Wigan Athletic, after two years at the JJB Stadium, and has signed a three-year contract at the Stadium of Light, replacing Ricky Sbragia.
The former Manchester United defender cut short a vacation to hold talks with Black Cats chairman Niall Quinn after he was granted permission to open discussions by the Latics.
Bruce's first press conference as Sunderland manager will be screened live on Sky Sports News at 6pm on Wednesday.
Quinn said on Sunderland's official website: "Steve will bring a professionalism and strength of character to this club that will really help to bring us forward to where we all want to be.
Compensation"He knows more than anyone what football means to people of this region and I'm confident that he will be able to instil into our players exactly what it means to play for this football club."
A statement on Wigan's official website read: "A compensation fee has been agreed between the two clubs, freeing Bruce to move to the Stadium of Light.
"The deal also includes assistant manager, Eric Black."
Latics chairman Dave Whelan said: "Everyone associated with Wigan Athletic is devastated that Steve and Eric have gone, we would be lying if we said any different.
"But things can change very quickly and I have always said I would not stand in anyone's way who wishes to leave the club, as long as the terms are in the best interest of Wigan Athletic.
"What Steve has achieved here over the past 18 months has been magnificent. After a period of instability, he put the team in order and started laying the foundations for a prosperous future.
Replacement"We finished in our second highest ever league position this season and this is something we will be looking to build upon going forward.
"As for a new manager, we have several options to consider and we will be talking to clubs and candidates over the next seven days.
"We will not rush the appointment as it is a decision not to be taken lightly. We will make a statement when an appointment has been made."