The Republic of Ireland keeper signed a £20,000-a-week, three-year contract to join on a free transfer from Coventry.
Westwood has worked his way back up the league after being released by City as a teenager.
After previous spells at Oldham and Carlisle, he will have played in the top five English divisions when he takes his Premier League bow for the Black Cats next season.
The 26-year-old said: "Getting released by City as a 19-year-old was the kick up the backside I needed. It gave me the hunger and desire to prove a lot of people wrong.
"I've come here to play first-team football. I know it'll be a tough contest with the other lads who are vying for the shirt and it's all about competition."