Tarmey was born in Ardwick, Manchester, Lancashire. Shortly after his birth, he moved with his family to live in Bradford, Manchester, where he was also educated. Following the death of his father William in 1944 whilst driving an ambulance at the Battle of Arnhem during the Second World War, his mother Lilian remarried, to Robert Cleworth. Tarmey attended the Bradford Memorial School and the Queens Street School (which became the Philips Park Secondary Modern School). On leaving school, he was apprenticed to his stepfather, who was an asphalt spreader by trade. He also worked in the construction industry for a number of years.
In 1968, Tarmey gave up his job in the building industry to work as a nightclub singer and entertainer. In order to supplement his income, he took on work as an extra on shows such as Coronation Street, amongst others. Despite suffering a serious heart attack in 1976 and a stroke in 1977, he was eventually offered the role of Jack Duckworth, a character who would go on to become an institution in British soap operas. He underwent quintuple bypass surgery in 1987, and had a pacemaker fitted after suffering a second heart attack in 2002, which was used as a storyline in Coronation Street to explain his absence. He also developed sleep apnoea, disrupting his breathing while asleep.
Tarmey was an extra in the Granada TV adaptation of King Lear (1983) which starred Laurence Olivier in the title role.
He was an accomplished singer and released several albums. Three of them (A Gift of Love (1993), Time for Love (1994) and After Hours (1996)) appeared in the UK Albums Chart.
He was the subject of This Is Your Life in 1992 when he was surprised by Michael Aspel on the set of Coronation Street. He has also appeared on Lily Savage's Blankety Blank.
In April 2006, when he turned 65, Tarmey announced he was thinking of retiring, which prompted letters of protest from fans. In 2009, he wanted to leave his role in the long-running television series, Coronation Street, due to his multiple health problems, which included severe breathing problems. The show's producers, however, persuaded him to stay until the 50th anniversary, in December of the following year. News of his departure was announced on 9 April 2010. Commenting, he said, "I've had the most amazing 30 years playing Jack. Because of him I've made fantastic friends and travelled all over the world. I'll be sorry to say goodbye". Tarmey's departure was pushed forward to the 8 November 2010 episode because of his declining health; in this episode Jack died asleep in his chair in a manner similar to the death of Vera (although Jack had a storyline illness). This was revealed in What's On TV and several other television guides for that week. Tarmey was the second longest serving male actor in the show.
In a March 2011 interview with Nigel Pivaro Tarmey revealed he also had to leave the series because his son Carl had been diagnosed with a brain tumour in 2009.
Tarmey's autobiography, Jack Duckworth and Me: My Life on the Street and Other Adventures, was published in 2010.
In 1955, he met his future wife Ali in the local youth club. They wed in 1962, and had two children: Carl (born 1966) and Sara (born 1970). Tarmey suffered from poor health for many years, having a severe heart attack at the age of 35 and also a stroke when he was 36. He had heart bypass surgery twice, once in 1987 and again (following another heart attack) in 2002. He and his wife Ali lived in Ashton-under-Lyne. He also suffered from sleep apnoea due to breathing problems. Despite his multiple health problems, Tarmey refused to quit smoking. In May 2011 Tarmey revealed that he needed to undergo further heart surgery.
A Coronation Street spokesman confirmed that Tarmey died in Tenerife from a heart attack on the morning of 9 November 2012 at the age of 71.