The England Under 21 international underwent a medical at the Stadium of Light on Saturday morning before putting pen-to-paper on a long-term deal.
United will receive an initial £3.5million fee, which could rise to a maximum of £6million should various criteria be met.
Earlier in the summer it had looked as though Campbell was on his way to Hull City - with whom he helped gain promotion to the Premier League the season before last - but he has instead opted for a move to the Black Cats.
Campbell spent last season on loan at Tottenham, whom he moved to as part of the deal that took Dimitar Berbatov to United, but struggled for playing time.
Having made just nine starts during his White Hart Lane sojourn, Campbell will be hoping for substantially more playing time under Steve Bruce at Sunderland.
Campbell's impressive displays at the European U21 Championship caught the eye and he will aim for more of the same next term.