The Bermondsey Yards scheme has been put forward by Aviva Investors along with Sellar – the company behind the Shard.
A decision on an earlier version of the scheme – designed by Shard architects Renzo Piano Building Workshop – was deferred by Southwark's planning committee in summer 2020.
Aviva came on board in 2021, agreeing to purchase the site from Sellar.
Revised plans for a more modest scheme have been drawn up by John Robertson Architects (JRA) and Studio RHE and were considered by the planning committee on Monday night.
"In design terms the revised scheme is a significant improvement, adopting a more sensitive approach to the Vinegar Yard warehouse as a non-designated heritage asset, and as a result to this part of the Bermondsey Street Conservation Area," planning officer Terence McLellan told councillors.
He added: "The Bermondsey Street building will form a high quality building, landmarking the important junction of St Thomas Street, Snowsfields and Bermondsey Street."
Mr McLellan said the 11-storey block would "form an effective end stop to the emerging tall building cluster on the edge of North Bermondsey".
Addressing the committee, Toby O'Connor of the Old Bermondsey Neighbourhood Forum raised a range of objections, including harm to heritage and potential environmental impacts.
Russell Gray, also of the Old Bermondsey Neighbourhood Forum, contrasted the developer's proposals for the Vinegar Yard warehouse with his own restoration of a warehouse on the other side of Bermondsey Street.
"It is perfectly possible to treat this building with the respect it deserves," he said, attributing Sellar and Aviva's proposed extension to "sheer greed".
Nick Staddon of Aviva Investors told the meeting that the scheme "seeks to balance jobs, heritage and public realm".
He said that the revised proposals responded to "strong public feedback" not to build directly above the historic warehouse.
Mr Staddon told the committee: "Although smaller than originally proposed, our application still generates significant social and economic benefits" including 915 jobs in the completed scheme.
London Bridge & West Bermondsey ward councillor Emily Hickson addressed the committee to make representations on behalf of her constituents regarding the height of the proposed new building on Bermondsey Street, and to raise concerns about the proposed public space between St Thomas Street and Snowsfields.
Cllr Hickson warned that at more than twice the height of the existing building on the site, the proposed 11-storey building would "risk spoiling this special and unique area".
Summing up, committee chair Cllr Richard Livingstone said he understood concerns about the proposal and recognised the increase in height compared to current buildings on Bermondsey Street, but on balance considered it to be a good scheme.
Vice chair Cllr Kath Whittam described the warehouse side of the scheme as "infinitely better" than the proposal that came to committee three years ago, but she was less convinced by the Bermondsey Street building.
The committee unanimously resolved to grant planning permission.