Murray was born in Montreal, Quebec and attended John Abbott College and Concordia University. Prior to being elected mayor, he was a coordinator of health education, working with AIDS patients at a Winnipeg clinic. Murray served as city councillor for from 1990 to 1998. He was first elected to council as the candidate of an alliance called "Winnipeg into the '90s", defeating Sam Katz, another future mayor. A 1992 documentary film A Kind of Family followed the relationship of Murray with his foster son, a 17-year-old tough street kid.

He was elected mayor on October 28, 1998 with 50.5f the vote in a close race against grocer Peter Kaufman, who received 45f the vote. Murray was re-elected in 2002 over former councillor Al Golden. He made Winnipeg the world's largest city with an openly LGBT mayor until Bertrand Delanoë was elected mayor of Paris.

In 1999, when Winnipeg hosted the Pan American Games, Murray became nationally known across Canada. He gained a reputation as an urban advocate, bringing attention to the fiscal imbalance of the 1990s which left major cities underfunded.

On May 7, 2004, Murray announced that he would run in the 2004 Canadian federal election after several months of denying rumours to this effect. He ran as a candidate for the Liberal Party in the riding of Charleswood - St. James as one of the party's "star candidates".

On May 11, 2004, Murray announced his resignation as mayor of Winnipeg. In doing so, he became the first mayor in Winnipeg history to resign mid-term.

On June 28, 2004, Murray was narrowly defeated in his attempt to become a member of the Canadian House of Commons by Conservative Steven Fletcher. Murray sought election in a suburban riding despite the fact that his main support was in the city centre. Some believe that Murray hurt his credibility when he took credit for the construction of the Moray Bridge and the associated Charleswood Parkway during the election period, as he had previously opposed such work when on city council. One of Murray's pet projects, the Esplanade Riel footbridge which connected The Forks to St. Boniface, was attacked by Conservatives as a "million-dollar toilet" and an example of Liberal waste, since the bridge had cost 22 million, going 7 million over budget. The footbridge is now occupied by a Salisbury House restaurant which the Winnipeg Free Press described as a "raging success".

Murray defended Thomas King's novel Green Grass, Running Water on the CBC's Canada Reads 2004.

Murray was appointed by Prime Minister Paul Martin as chair of a National Round Table on the Environment and Economy in March 2005, despite opposition from other political parties and a non-binding vote against his appointment in the House of Commons. He now lives in Toronto where he lectures at the University of Toronto's Massey College.