McMahon was born in Miles Platting, Manchester, to William McMahon and Alicia O'Rourke (Breffni) . His father was a truck driver. The family moved from Cheetham Hill when he was a child to Middleton, where he attended secondary school. He left school at the age of 16.
McMahon started work in 1997 as an apprentice technician at Manchester University rising to become a senior technician before leaving in 2004. He then joined local government service as a regeneration officer and latterly as a town centre manager.
McMahon was first elected to Oldham Metropolitan Borough Council in November 2003 as a Labour councillor for Failsworth East ward. He held various posts on Oldham Council before becoming the council's Labour group leader in 2008 after the Liberal Democrats won control of the authority. At the 2011 local elections, Labour re-gained control of the council and McMahon became its leader. As council leader McMahon sat as one of the 11 members of the Greater Manchester Combined Authority with responsibility for transport.
McMahon was the inaugural chairman of the Co-operative Council Innovation Network and served as the Labour leader of the Local Government Association. McMahon was named the 6th most influential person in local government by The Local Government Chronicle ahead of senior government ministers.
In August 2014, McMahon was elected to represent Labour councillors on the party's National Executive Committee (NEC).
In the 2015 Labour leadership election, McMahon was reported to have supported Liz Kendall's bid to be leader. Kendall came last of four candidates with less than 5% of the vote.
In 2016 McMahon stood down as council leader and was replaced by his Deputy, Jean Stretton
McMahon won the selection to be Labour Party candidate at the Oldham West and Royton by-election following the death of incumbent Michael Meacher.
At the by-election held on 3 December 2015, McMahon was elected Member of Parliament for Oldham West and Royton, with 62% of the vote – an increase of seven percentage points since the 2015 general election. At the by-election McMahon represented just the Labour Party rather than his later Labour and Co-operative Party affiliation.
He served as Parliamentary Private Secretary to the Deputy Leader of the Labour Party until being appointed to serve as Shadow Minister for Local Government and Devolution.
In February 2014 McMahon was named "Council Leader of the Year" during the Councillor Achievement Awards hosted by the Local Government Information Unit. He was credited with leading improvements in Oldham Metropolitan Borough Council having redesignated it as a Co-operative Council. Also in 2014, University Centre Oldham conferred upon him Honorary Fellowship, as well as being elected a Fellow of the Royal Society of Arts.
McMahon was appointed Officer of the Order of the British Empire (OBE) in the 2015 Birthday Honours for "services to the community in Oldham", and was invested by Charles, Prince of Wales on 18 December 2015.
McMahon lives with Charlene Duerden in Failsworth and they have two children.