The Labour councillor, who has been leader for five years, will step down on Thursday 10 September and a new leader will be appointed that day.
Mr Matheson said the "time is right" to "progress to the next phase in my career".
It is believed Mr Matheson wishes to stand as a candidate for next year's Scottish Parliament elections.
Mr Matheson stood as a candidate in the Scottish Labour deputy leadership contest but lost out to Fife MSP Alex Rowley when the results were announced on Saturday.
He said: "The decision I have announced today was made by me some weeks ago. By confirming the date, the process can begin to effect a smooth transition to a new leader in time for the next meeting of the full council.
"Being leader of the city I love has been the greatest honour of my life. It is not a job for the faint hearted, especially given the budget cuts we have had to contend with, but I would not have missed this experience for the world."
Mr Matheson, who was first elected to the city council in 1999, will remain as ward councillor for Anderston/City but will not stand again in the 2017 council elections.
Labour, which has had overall control of Glasgow City Council since 1980, had 45 of the city's 79 councillors at the last election in 2012.
However, the city of Glasgow voted in favour of independence at last year's referendum and Labour lost all its MPs in the city to the SNP at the general election in May.
This was not really a surprise. Mr Matheson had been making it clear for weeks that he was planning to step down after the Scottish Labour leadership election. The only question was exactly when.
Looking back, many will be surprised that he lasted as long as five years in the post.
If you think back to the 2012 council elections, a lot of people had almost written off Labour's chances of holding on to Glasgow City Council in those elections. So there was a great surprise, within the Labour party even, when Labour retained its overall majority on Glasgow City Council.
Before the 2012 elections, a lot of people imagined Councillor Matheson would be out as a leader after that but following that result it reinforced his position.
Mr Matheson's supporters would point to the successful delivery of the Commonwealth Games and the Â£1bn city deal but he has also been a divisive figure at times.
A plan for a radical redevelopment of George Square was abandoned amid some acrimony and he also survived an embarrassing incident when he was caught cheating on his partner.
Susan Aitken, the SNP group leader on the council, said that while there had been "disagreements over policy and strategy, no-one could doubt Gordon Matheson's commitment to Glasgow".
She said: "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.
"He deserves our thanks for his years of public service and I and the members of the SNP group in the City Chambers wish him well in whatever he chooses to do in future."
The leader of Glasgow City Council, Gordon Matheson, has announced he will stand down next month.