Born of Irish heritage (his immediate family hailed from County Cork), Coleman was a keen amateur runner. He attended a grammar school in Cheshire. In 1949, he won the Manchester Mile, the only non-international runner to do so. He ran 440 yards for Staffordshire and injury eventually caused him to give up competitive running. He later became president of the Wolverhampton & Bilston Athletics Club.

He worked as a reporter for the Stockport Express, and during military service worked for the British Army Newspaper Unit. Part of his time in National Service was carried out in Kenya.

He joined Kemsley Newspapers after demobilisation and at twenty two became editor of the Cheshire County Express. He didn't attend the 1952 Olympic trials because of hamstring injuries. Instead he approached the BBC to see if they would like any help with athletics coverage. Although he did not have an audition, the BBC asked him to cover Roger Bannister at Bradford City Police Sports. The following year he began freelance radio work in Manchester.

In 1954 Coleman moved to Birmingham and joined the BBC as a news assistant and sports editor. His first television appearance was on Sportsview, coincidentally on the day that Roger Bannister broke the four-minute mile. In November 1955, he was appointed Sports Editor for the BBC's Midlands Region.

In October 1958, the BBC's Head of Sport Peter Dimmock recruited Coleman to be the presenter of the new Saturday afternoon sports programme Grandstand. He continued as the regular presenter until 1968. He also presented the BBC's Sports Review of the Year from 1961, and Sportsnight with Coleman (1968–1972) - which included an interview with the then Conservative Party leader, Ted Heath, on his famous triumph in the Sydney to Hobart yacht race - as well as other special sporting events such as the Grand National. He even covered the return of The Beatles from the United States and the 1959 General Election for the BBC from the Press Association headquarters.

As well as a presenter, Coleman was also a sports commentator. He presented and/or commentated on 11 Olympic Games from Rome 1960 to Sydney 2000, as well as eight Commonwealth Games and several World Cups, including the finals of 1974 and 1978.

He was the BBC's senior football commentator for several years from 1971; he commentated on the FA Cup final from 1972 to 1976 inclusive, although missed the 1977 game because he was in a legal dispute with the BBC, allowing John Motson to make his FA Cup final debut. Coleman returned for the 1978 final before Motson took over the following year. Coleman continued to work at football matches as a secondary commentator until 1981.

In 1968, at the Mexico Olympics Coleman was recorded at 200 words per minute while commentating on David Hemery's win in the 400 m Hurdles. After the finish he could only identify the first two and famously exclaimed: Who cares who's third? The bronze medal winner turned out to be another Briton, John Sherwood. Out of respect for Sherwood, most subsequent showings of the race have dubbed the line out. He also had to commentate on a Greek athlete called Papagiorgiopoulos and a Madagascan athlete called Jean-Louis Ravelomanatsoa in adjacent lanes in the 100m.

Coleman's inability to 'read' a race remained entirely unsullied by experience to the end of his long commentating career. The phenomenon was clearly spotted by satirists of the '80s and '90s, who portrayed him as constantly surprised by mundane happenings at athletic events. Clive James wrote that the difference between commentating and 'colemantating' is that a commentator says something you may wish to remember; a colemantator says something you try to forget.

In 1972, he broadcast for several hours during the siege at the Munich Olympics as well as the memorial service days later.