In 1987, he was chosen to captain the England B team in a match against the full national team of Malta, but it was to be his only appearance in an England shirt, and he has subsequently been described as one of the best defenders of his era never to be selected for the full England team. Bruce later stated, "I bumped into former England manager Bobby Robson in Benfica (sic). He came up to me and said 'I should have capped you'. It was nice to hear but it still didn't get me one .... I'll always be a little disappointed I didn't get one."
Bruce began to attract the attention of big-name clubs in late 1987, with Manchester United, Tottenham Hotspur, Chelsea and Rangers all reported to be interested in signing him. Manchester United quickly emerged as the front runners for his signature, and Bruce publicly expressed his desire to sign for the club. The deal came close to collapsing when Norwich asked for a transfer fee of £900,000 after initially agreeing to accept £800,000, leading to Bruce refusing to play any further matches for the club, which he felt was jeopardising his dream move. On 17 December 1987, shortly before his 27th birthday, the deal was concluded and Bruce officially left Carrow Road, for a fee reported as £800,000 or £825,000. Norwich fans remembered his contribution, and in 2002 voted him into the Norwich City Hall of Fame.
Bruce made his Manchester United debut in a 2–1 win over Portsmouth on 19 December 1987, and played in 21 of United's remaining 22 league fixtures, helping the club to a top-two place in the First Division for the first time since 1980. The team only finished in mid-table in the following season, prompting manager Alex Ferguson to bring in several new players, including Gary Pallister, who joined the club in August 1989 from Middlesbrough. His partnership with Bruce in the centre of defence was described in 2006 by the then-United captain, Gary Neville, as the best in the club's history. "Dolly and Daisy", as the pair were affectionately known, are described as "arguably the best" on the official Manchester United website. Bruce and Pallister were part of the team that won the 1990 FA Cup Final against Crystal Palace in a replay.