Johnston made his first team debut for Middlesbrough, aged 17, in a FA Cup tie against Everton. His league debut came on 4 February 1978 in a 2–1 victory over Birmingham City at St Andrews and he scored his first goal later that season in a 2–1 home league defeat to West Ham United. Johnston scored 16 goals in 64 games for Middlesbrough before moving to Liverpool in 1981 for £650,000.

Johnston made his Liverpool debut in August 1981, coming on as sub for Ray Kennedy in the 1–0 league defeat to Wolverhampton Wanderers at Molineux. Johnston’s first start came in the Intercontinental Cup fixture against Brazilian side Flamengo.

Johnston scored his first goal for Liverpool on 8 December 1981 against Arsenal at Anfield, during a League Cup fourth round replay. Johnston opened the scoring in the fifth minute of extra time in a 3–0 win. Johnston, known as Skippy, was a crowd favourite at Anfield during his long spell with the club. He worked under three managers – Bob Paisley, Joe Fagan and Kenny Dalglish – and, when picked, predominantly played on the right side of midfield. He made a total of 271 appearances for the club and scored 40 goals.

Johnston was approached by Jock Stein in the early 1980s with a view to him playing for Scotland as he was eligible through his father. Johnston declined Stein’s offer and also resisted calls to play for his country Australia in 1981 and 1984. He instead chose to represent England at under-21 and ‘B’ team level. Early in his career in England he had described playing football for Australia as “like surfing for England.” Johnston was also eligible to represent the South African national side due to being born there but was never approached or offered by the South African federation to play for them.

Johnston was part of the League championship-winning teams of 1982 and 1983 and gained a League Cup winner’s medal in 1983. In 1984, Johnston was part of the team which won a treble of League championship, League Cup and European Cup. Two years later he was an integral part of the side which won only the third League championship and FA Cup “double” of the 20th century. In the 1986 FA Cup final at Wembley, Johnston scored Liverpool’s second goal in a 3–1 win over Everton.

Johnston was called up to the full England squad in November 1987 but did not make an appearance at that level.

In 1988, he was a frequent substitute and occasional starter as Liverpool again won the League title and reached the FA Cup final, aiming to complete a second “double”. Johnston wrote the club’s traditional Cup final song called “Anfield Rap” which combined pro-Liverpool lyrics with the rap and house trends of the time, with other Liverpool players contributing.

When the Hillsborough disaster occurred in 1989, a year after Johnston’s departure, he raised funds in Australia and also flew back to England to attend funerals and memorial services. He later dedicated his autobiography, titled Walk Alone, to the victims of the Heysel and Hillsborough disasters.

In 1991, when Graeme Souness was manager of Liverpool F.C., he asked Johnston if he would like to train with the team with a view to playing again. Liverpool F.C. still held Johnston’s registration as a player. It didn’t work out and Johnston moved on. However, Johnston possesses an undying love for Liverpool and its fans. After his retirement he was constantly being linked to clubs from all over. Johnston always retorted this speculation stating that he could never play for anyone other than Liverpool.

Though he travels the world with his business interests, Johnston remains based in Australia. He has been recognised at home for his achievements in England. On 18 June 2006, Johnston made an appearance as a guest on The Footy Show World Cup Spectacular in Germany revealing information on his career.

During the 2006 poll 100 Players Who Shook The Kop compiled by the official Liverpool FC website, over 110,000 of the club’s fans worldwide voted for their top 100 players of all time, with Johnston coming in a very respectable 59th.

During the 2010 FIFA World Cup, Johnston wrote a 12-page letter to FIFA president, Sepp Blatter, in which he collected all criticism by players and coaches of the controversial Adidas-produced Jabulani ball, risking his reputation, and expecting to be blacklisted by the conservative governing body as a result of this letter.