Sbragia has signed an 18-month contract and said that he was happy with its relatively brief length.
"It doesn't feel good after losing, but I'm really looking forward to it, looking forward to the challenge ahead," he said. "The ambition at present is just to stay in the Premier League. I'd done a lot of thinking in the weeks previously, it was going well for us and in the last couple of days it was finalised in my mind that [the permanent role] was what I wanted to do. I was enjoying it."
He is expected to make signing a defender a priority next month, as well as trimming Sunderland's large squad.
"I'll have a chat with the coaching staff and with the window opening up [analyse] what we think we need," Sbragia said.