The 59-year-old former Aston Villa, Leicester and Celtic boss has signed a three-year contract with Sunderland.
O'Neill said: "It's a very nice feeling to be back in football and to be the manager of Sunderland. It's a big moment for me.
"I'd heard about what a good club it was but coming here, seeing the stadium and training ground, I've been bowled over. It's absolutely fantastic.
"I hope I can help Sunderland to very successful period. That's what I've come for and that's my driving ambition."
Sunderland chairman Ellis Short told the club's official website: "Martin has as good a managerial pedigree as you could wish to find and has proven over the years to be a very astute, top-level manager.
"During his time at Aston Villa he established the club firmly in the top ten of the Barclays Premier League year-on-year and this is something we are striving to achieve at Sunderland.
"Having spoken with Martin over the last two days I know he is brimming with enthusiasm and anticipation about the challenge of taking Sunderland forward and I believe he is the perfect choice to deliver the success we all desire."