In the 1954–55 season, he was spotted by Archie Beattie, a scout for Huddersfield Town, who invited 14 year-old Law to go for a trial. When he got there, the manager said, “The boy’s a freak. Never did I see a less likely football prospect – weak, puny and bespectacled.” However, to Law’s surprise, they signed him on 3 April 1955. While he was at Huddersfield, he had an operation to correct his squint, which greatly enhanced his self-confidence.

Huddersfield’s relegation to what was then the Second Division made it easier for Law to get a game, and he made his debut on 24 December 1956, aged only sixteen, in a 2–1 win over Notts County. Manchester United’s manager Matt Busby shortly offered Huddersfield £10,000 for Law, a substantial amount of money for a teenage footballer at that time, but the club turned the offer down. Bill Shankly was manager of Huddersfield between 1957 and 1959, and when he left for Liverpool he wanted to take Law with him, but Liverpool were unable to afford him at that time.

Law was not chosen to play for Scotland in the 1958 FIFA World Cup, but was given his debut in a British Home Championship match against Wales on 18 October 1958 by Matt Busby, who managed Scotland on a temporary basis for two matches. Law scored Scotland’s second goal in a 3–0 win over the Welsh at Ninian Park. He played but did not score in Scotland’s match against England on 15 April 1961. Scotland lost the match 9–3, and Law described it as his “blackest day”. While with Torino, Law continued to play for Scotland, although the club were not keen to release him for international matches and had put a clause into his contract stating that they were not obliged to do so.

In March 1960, Law signed for Manchester City for what was then a British record transfer fee, estimated to be £55,000, although Law’s share of the fee was “precisely nothing”. Once again, Matt Busby had attempted to sign Law for Manchester United, but United’s cross-city rivals beat them to Law’s signature.

City had narrowly avoided relegation from Division I the previous season, and Law genuinely felt that Huddersfield had a better team at the time. He made his debut on 19 March, and scored in a 4–3 defeat to Leeds United. In April 1961, he scored two goals in a 4–1 win over Aston Villa that ensured City’s survival in Division One.

Although he had thought about leaving, he was playing well and in 1961 Law scored an incredible six goals in an FA Cup tie against Luton Town. However, the match was abandoned with twenty minutes to go, so his six goals did not count. To make matters worse for him, Luton won the replay 3–1, and City were knocked out of the Cup.

On 7 February 1962, he was injured in a car crash when his teammate Joe Baker drove the wrong way around a roundabout and clipped the kerb as he tried to turn the car around, flipping it over. Baker was almost killed, but Law’s injuries were not life-threatening.

By April, he had put in a transfer request, which was ignored. The final straw for Law came in a match against Napoli when he was sent off. After the match, he was told that Torino’s coach, Beniamino Santos, had instructed the referee to send him off because he was angry at Law for taking a throw in, which he had been told not to do. Law walked out, and was told that he would be transferred to Manchester United. A few days later, however, he was told that he was being sold to Juventus and that the small print in his contract committed him to going there whether he wanted to or not. He responded by flying home to Aberdeen, knowing that Torino would not get a penny in transfer fees if he refused to play at Juventus. He eventually signed for United on 10 July 1962, for a new British record fee of £115,000.

Law moved back to Manchester, boarding with the same landlady with whom he had lived during his time as a City player. His first match for United was against West Bromwich Albion on 18 August 1962, and he made an excellent start, scoring after only seven minutes. The match finished in a 2–2 draw. However, United’s form had been erratic since the Munich air disaster in 1958, and because of their inconsistency they spent the season fighting relegation. In a league match against Leicester City Law scored a hat trick but United still lost. They found form in the FA Cup though, with Law scoring another hat trick in a 5–0 win against his old club Huddersfield Town, and they went on to reach the final against Leicester City. Leicester were strong favourites, having finished fourth in the league, but Law scored the first goal as United won 3–1 in what turned out to be the only FA Cup final of his career. He also married his wife Diana that season, on 11 December 1962.

An incident took place that season that Law felt had repercussions in later years. In a match against West Brom on 15 December 1962, the referee Gilbert Pullin consistently goaded Law with taunts such as “Oh, you clever so and so, you can’t play”, and after the match, Law and his manager Matt Busby reported the matter to the Football Association. A disciplinary committee decided that Pullin should be severely censured, but he did not accept their verdict and quit the game. Law later claimed that “in the eyes of some referees, I was a marked man” and blamed the incident for the “staggeringly heavy punishments” that he received later in his career.

He first met his wife-to-be, Diana, in an Aberdeenshire dancehall when they were both still teenagers. They married in December 1962 and went on to have five children. Their daughter, also called Diana, worked for several years in the Manchester United press office. Their other children are Gary, Andrew, Robert and Iain. Denis Law and his wife still live in the Manchester area.

Law was chosen for the Rest of the World team that faced England in the FA Centenary match in 1963.

The following season, Law injured his right knee while playing for Scotland against Poland on 21 October 1965. He had previously had an operation on the same knee while at Huddersfield, and the injury was to trouble him for the rest of his career.

Law injured his right knee while playing for Scotland against Poland on 21 October 1965. Law scored in Scotland’s famous 3–2 victory over England on 15 April 1967 in the 1967 British Home Championship, less than a year after England had become world champions. Manchester United won the league that season, but Law felt that the victory over England was even more satisfying.

In 1966, Law asked United’s manager Matt Busby to give him a pay rise at his next contract renewal, and threatened to leave the club if he did not get one. Busby immediately placed Law on the transfer list, announcing that “no player will hold this club to ransom, no player”. When Law went to see him, Busby pulled out a written apology for him to sign, showing it to the press once he had done so. Law later claimed that Busby had used the incident to warn other players not to do the same thing, but had secretly given him the pay rise. Despite all this, Law scored 23 goals in 36 league appearances during 1966–67, helping United win the league title again.

In 1968, United won the European Cup for the first time, but Law’s knee injury was causing him serious problems and he missed both the semi-final and the final as a result. He was regularly given cortisone injections to ease the pain, but playing while the knee was still injured was causing long-term damage. He visited a specialist in January 1968 who wrote to United claiming that a previous operation to remove the cartilage from the knee had failed and recommending that a second operation be performed, but Law was not shown the report for several years and had to continue full training.

Wilf McGuinness took over as first team coach at the start of the 1969–70 season. United finished eighth in the league, but Law missed almost all of the season through injury, and in April 1970 he was transfer listed for £60,000. Nobody made a bid for him, so he stayed at United.

Law had a contract with Manchester City for the 1974–75 season, but new manager Tony Book told him that he would only be playing reserve team football if he stayed at the club. He did not want to end his career in this way, so he retired from professional football in the summer of 1974. Law played two games for Manchester City in the season 1974–75, in the pre-season Texaco Cup tournament, scoring the last goal of his career in the game against Sheffield United at Bramall Lane on 6 August 1974. His last professional game was the 2–1 victory against Oldham Athletic at Maine Road on 10 August 1974. He formally retired on 26 August 1974.

Since retiring as a player, Law has often worked on radio and television summarising and presenting games. Law was one of the first sport news presenters of Granada Reports and was the sub-presenter of Granada Television’s Match Time, the equivalent of LWT’s The Big Match. He appeared as a special guest on the TV guest show This Is Your Life on 19 February 1975, months after retiring as a player.

Law was made an Inaugural Inductee of the English Football Hall of Fame in 2002 in recognition of his impact on the English game. On 23 February 2002, a statue of Law (alongside George Best and Bobby Charlton) was unveiled at Old Trafford, in the part of the stadium known as the Scoreboard End. He had a successful operation to treat prostate cancer in November 2003 and was awarded honorary degrees from the Universities of Aberdeen and St. Andrews in 2005, and Robert Gordon University in 2017.

On 25 November 2005, Law was at the bedside of former United teammate George Best as he died of multiple organ failure.

In May 2008, at the City of Manchester Stadium, Law (with UEFA president Michel Platini) presented the medals to the winners of the UEFA Cup, Zenit Saint Petersburg and their opponents, Scottish side Rangers.

In February 2010, Law was named as patron of the UK based charity Football Aid, taking over from the late Sir Bobby Robson.

In 2012, a statue to Law, commissioned by the Denis Law Legacy Trust, was unveiled at the entrance to Aberdeen Sports Village (a facility he had formally opened two years earlier) depicting his pose after scoring for Scotland against England in 1967.

Law was appointed Commander of the Order of the British Empire (CBE) in the 2016 New Year Honours for services to football and charity. In 2017, Law received the Freedom of the City of Aberdeen.