Mr Matheson, who stood unsuccessfully for the deputy leadership of the Scottish Labour Party, will end his five-year tenure in charge of the local authority on 10 September, and a new leader will be appointed at a council meeting on that day.
Mr Matheson said he feels the “time is right” for him to “progress to the next phase” of his career. One option that is likely to be explored by Mr Matheson is attempting to enter Holyrood as an MSP.
The announcement comes three days after Mr Matheson lost a bid to become deputy leader of Scottish Labour, with Alex Rowley securing the post when the results were announced on Saturday.
Mr Matheson has been leader of Glasgow City Council since 2010 and last month was awarded a CBE by the Queen for services to local government and the community. He said: “One of the judgments of politics is to know when to move on. The time is right for me to consolidate the successes I have enjoyed in Glasgow in recent years and progress to the next phase in my career.
“Glasgow is Scotland’s big success story. There is a buzz about this city. We have a great international reputation following the delivery of the best ever Commonwealth Games. Our population is growing again and educational attainment in the city is improving every year.
“Personal highlights of my time as leader include welcoming Pope Benedict to Glasgow, leading Labour to an overall majority victory at the 2012 council elections, speaking at the opening ceremony of the Commonwealth Games, and successfully negotiating the biggest City Deal in the UK that will create 29,000 new jobs. Undoubtedly the lowest points were the Clutha helicopter tragedy, and the Queen Street bin lorry crash. We will never forget those who lost their lives or were injured, and our hearts go out to the families and loved ones whose lives were changed forever.
“The selfless and generous response of the emergency and public services, and the people of Glasgow, helped the city to deal with these tragedies with dignity and resilience.”
Mr Matheson, who was first elected to the council in 1999, plans to remain as ward councillor for Anderston/City but will not stand again in the 2017 council elections.
Glasgow City Council SNP group leader Susan Aitken said: “Although we had disagreements over policy and strategy, no-one could doubt Gordon Matheson’s commitment to Glasgow. He worked in partnership with the Scottish Government to deliver the best ever Commonwealth Games in the city and their legacy has the potential to benefit Glasgow for many years to come.”