Lambeth's planning application committee considered the scheme at its meeting on Tuesday evening.
The site is currently occupied by a Texaco petrol station and is owned by engineering firm Hotchkiss Ltd with the development being managed by Ocubis.
The latest scheme – designed by Hopkins Architects – includes two new linked buildings of 26 and 29 storeys.
Each tower would comprise a separate hotel, with 516 bedrooms in the south tower and 356 in the north building.
The adjacent Vintage House building would gain a two-storey extension and remain in office use.
Vauxhall ward councillor Isla Wrathmell told the committee that the area needed a "thriving high street and strong community" rather than being a "feeder for London's key tourist areas".
Noting the presence of other nearby hotels, she said: "Although their contribution is welcome, we do not need another one."
Cllr Wrathmell added: "These two towers will further reduce the daylight and sunlight in an area of already low daylight and sunlight levels.
"There will be a particularly significant ... impact on Peninsula Heights, which this development would overlook, as well as privacy concerns."
Asked about the likely nature of the hotels, Stephen Chatfield, development director at Ocubis, declined to name the prospective operators but said they would be "bottom end of four star, maybe three star".
He added: "We're trying to provide a very well-designed... slightly smaller room and the hotel is very well located for people spending money in Lambeth."
Committee member Cllr Martin Bailey said he preferred the latest scheme to the version approved in 2020: "The design is much better and more appropriate for the site," he said.
The committee unanimously adopted the planning officers' recommendation that planning permission be granted.