The announcement came following a city-wide strategic housing market assessment (SHMA) for the draft London Plan, which is set to be published next month,
Speaking to Planning, James Murray, the deputy mayor for housing, said the SHMA showed an overall need for London of 66,000 homes a year but the capacity identified was 65,000.
"So we’re pretty much hitting the need," he said.
The current version of the London Plan set the capital's ten-year housing target at 42,000 homes a year, but outlined an annual housing need of between 49,000 and 62,000.
The shortfall was criticised in 2014 by the planning inspector examining the document, who called for then mayor Boris Johnson to "engage" with Home Counties councils to help deal with the overspill.
Despite the lack of such a significant shortfall in the new draft, Murray said co-operation between the GLA and its neighbours on delivery of new housing would continue: "There’s a lot of ongoing discussions with the wider South East about how we work together, about increasing housing based on greater investment in transport infrastructure. Both London and the wider South East need to be building more housing."
He also said the GLA's SHMA was not informed by the government’s proposed new method of calculating objectively-assessed housing need. Published in September, the consultation document suggested that London has an annual housing need of 72,000 homes a year.
Murray said: "We will be responding formally to the government on their new method.
"I think they will recognise that the assessment of need we’ve come up with was based on an analysis that was started some time ago and is well over London's previously-assessed need.
"What’s important is that, on the basis of our already-ambitious numbers, we get on and produce a plan that can support that delivery and growth."
Murray also confirmed that the draft London Plan will include the mayor’s strategic target of 50 per cent affordable housing, though the SHMA had identified an affordable need of 65 per cent of new housing.
The mayor is "committed" to the "very ambitious" 50 per cent target, he said, adding that any target needed to be "achievable in terms of viability and public funding".
He said: "The scale of ambition in the London Plan, based on the SHMA, really represents a huge step change in what we are trying to achieve."