Acorn Property Group and Galliard Homes are behind the proposal – designed by SPPARC architects – for the 33-36 Bear Lane site just north of Dolben Street in Bankside.
The developer says the scheme will provide work space for 520 jobs.
Former occupants of the site included silversmiths Grant Macdonald and a theatrical scenery company.
20 years ago the Grant Macdonald workshop produced the orb and cross gifted to Dresden as a symbol of reconciliation and placed atop the dome of the restored Frauenkirche.
Introducing the scheme, planning officer Philip Ridley said: "Although it is acknowledged that there will be impacts on neighbouring residents, we do believe that this is an acceptable impact, and that – on balance – the benefits of the scheme outweigh the negatives."
Mr Ridley also emphasised the scheme's contribution to achieving Southwark Council's policy to develop the 'Low Line' pedestrian route along the railway viaducts that cut across the borough.
Dolben Street resident Gregory Simmons told councillors that the scheme was "overbearing" and that the "the massing is grossly inappropriate for a narrow residential lane".
Neighbour Tony Quinn added: "This building is simply too big and out of character.
"It will be an immense burden on over a hundred local residents; families who've lived here for over a decade whose privacy will be invaded and natural light severely diminished."
Mr Simmons asked the developers to consider refurbishing the existing buildings instead of demolishing them.
Representing the applicant, Julian Hampson from Acorn Property Group said: "The proposal before you is the result of over four years of dialogue with council officers.
"There have been four rounds of public consultation. Since the application ... we've made substantial amendments to the format and architecture to deal with the issues which are arising."
Mr Hampson said that the development would fund the provision of an additional Santander Cycles bike hire docking station in the area.
Architect Trevor Morriss described the scheme as "a proposal that respects and responds to the setting of the street to create a building that skillfully cohabits with the neighbouring properties whilst mitigating matters of privacy and amenity".
He said that the architect "reflects the industrial heritage of the area, adopting a modern warehouse aesthetic".
Borough & Bankside ward councillor David Watson addressed the committee to object to the scheme. He said: "Bluntly, we don't need more office blocks in Borough & Bankside.
"We need affordable homes and green community spaces.
"This development was conceived pre-pandemic and now risks blighting the neighbourhood with an oversized monolith that will join the myriad other office blocks sitting half-empty across my ward."
As councillors debated the application, planning committee chair Cllr Richard Livingstone said: "This is clearly a complicated site."
"I think the big challenge is, given the narrowness of Bear Lane, 'What could be built there that would both make sense economically for whoever was developing it, and would not have some of those impacts in terms of daylight and sunlight?'"
He added: "It's clear the developer has made a number of steps to try to address people's concerns in terms of privacy and in terms of daylight and sunlight."
When voting on the application, the committee's vote was tied, with two votes in favour, two votes against and one abstention. Committee chair Richard Livingstone used his casting vote to approve the application.