Born in Cowcaddens, Glasgow, Nicholas grew in the Maryhill area of the city (specifically the Wyndford estate) where he was a childhood friend and neighbour of fellow footballer Jim Duffy.
[9] He made his first team debut at 17 years of age on 14 August 1979 in a Glasgow Cup tie against Queens Park, scoring Celtic's second goal in a 3–1 win.
[13] Nicholas began to feature regularly for Celtic, and on 30 August scored his first goals in major competition when he netted twice during a 6–1 win over Stirling Albion in the Scottish League Cup.
[14][15] Playing up front alongside one of either Frank McGarvey or George McCluskey, he went on to score 20 goals in 23 games up to the end of December 1980.
[15] He continued to score regularly after the turn of the year,[15] including two goals against Rangers in February 1981 as Celtic came from behind to win 3–1 and go top of the league.
[20] Nicholas returned to the team for the start of season 1982–83 in August 1982, playing in all six matches of the group stages of the 1982–83 Scottish League Cup, scoring seven goals as Celtic qualified with ease, including a four-goal haul in a 7–1 rout of Dunfermline.
He evaded two tackles from Ajax defenders before curling an excellently placed left-foot finish past goalkeeper Piet Schrijvers.
His partnership up front with Frank McGarvey helped Nicholas become the leading goalscorer in Scotland and one of the best strikers in the British game.
[14][26] In the final league match of the season, Nicholas scored twice from penalty kicks as Celtic recovered from a 2–0 deficit at half-time against Rangers to win 4–2.
[29] Terry Neill signed Nicholas for Arsenal on 22 June 1983 for a transfer fee of £750,000 (£3,200,000 today), making him at the time the second most expensive export from the Scottish league.
[31] He made his competitive debut for Arsenal in the opening league match of the season on 27 August 1983 at Highbury against Luton Town.
Former Scotland international Ian St John said that Nicholas showed he was a player of "genuine class" and that there was a "buzz of excitement every time he moved on to the ball".
[34][35] By this time Arsenal had endured a slump in form and were lying sixteenth in the First Division, resulting in the sacking of manager Terry Neill on 16 December 1983.
[38] Under new manager Don Howe, Arsenal improved in the second half of the season and eventually finished in sixth place.
[49] He was dropped from the Arsenal team four games into the start of the 1987–88 season, in favour of Perry Groves as the strike-partner for new signing Alan Smith.
[40][44] Nicholas joined Aberdeen in January 1988 for a transfer fee of £400,000 (£1,350,000 today),[44] stating his desire to get his career back on track.
[50] The arrival of Dutch forward Hans Gilhaus in November 1989 saw the pair immediately form a good partnership up front.
The arrival of new manager Liam Brady at Celtic in 1991 saw an improvement in fortune for Nicholas, and he went on to score 21 league goals during season 1991–92.
[14] On 21 March he opened the scoring at Ibrox in a 2–0 win over Rangers; taking a long ball from a Chris Morris free kick, he volleyed home a powerful shot past goalkeeper Andy Goram.
[14] A week later on 28 March, he ran across the Dundee United defence 25 yards out and suddenly chipped the ball past an unsuspecting Alan Main.
[14] In July 1995 Nicholas joined Clyde on a free transfer, where he spent one season and scored five times in 31 league games before retiring as a player.
The last of his five goals for Scotland had come on 17 October 1984 in a 3–0 win over Iceland at Hampden Park early in the World Cup qualifying stages.