The 21-year-old was also being tracked by Hull City, where he enjoyed a successful loan spell during the 2007/08 season, but signed a four-year deal with the Black Cats.
Campbell spent most of last season on loan at Tottenham Hotspur, where he helped the team reach the Carling Cup final before being ruled ineligible to face United - who went on to win on penalties.
The Huddersfield-born player came through the ranks at Old Trafford before going on loan to Royal Antwerp at the start of the 2006/07 season.
Success in Belgium was recognised by Sir Alex Ferguson, who handed Campbell his debut as a substitute in the derby against Manchester City at Eastlands in August 2007.
Campbell then went on loan to Hull and helped them win promotion to the Premier League. It had appeared he would make a permanent move to the KC Stadium when the clubs agreed a fee earlier this summer but Sunderland beat them to it.
After missing out on the striker, Hull manager Phil Brown said: "I'm disappointed but I was always nervous about the deal because of the way it was dragging along."
Campbell also caught the eye at this summer's European U21 Championship in Sweden as England reached the final, where they were beaten by Germany.