The council says it will introduce temporary prohibitions on the Tooting Common cycle route for up to six months from 12 September 2017 to enable the work, which involves removing 51 trees, relocating three others, and planting 64 replacement and new trees, using a Heritage Lottery Fund grant.
In a letter to residents, the borough's director of environment and community services Paul Chadwick said: "The works involved were unanimously recommended by the Community Services Overview and Scrutiny Committee of 20 September 2016.
"Those recommendations, to replace the existing horse chestnut trees with an avenue of new trees, were made after an extensive public consultation exercise which resulted in 74% of respondents expressing support for the option of complete replacement of the trees as a single operation."
He added: "Due to publicly-made suggestions, via the internet, that the works should be disrupted, we are not giving advice notice of the exact date of the commencement date of the works within the six months’ period."
But a petition against the planned felling of the avenue, first planted around 1870, has been signed by more than 5,400 people, while some have threatened to chain themselves to the trees. Local MP Rosena Allin-Khan has also voiced her opposition.
Arboricultural consultant Jeremy Barrell, who has been following the case, said: "I inspected the trees this month and I would stake my professional reputation on there being no valid reason to fell them.
"Most of the trees do need minor intervention pruning, but this is no more than would be expected during normal maintenance for trees of this size and location."