The scheme by developer CLI Dartriver - designed by architects Lifschutz Davidson Sandilands - was considered by a Southwark Council planning committee on Tuesday evening.
Planning officer Gemma Parry explained that the existing building occupies an L-shaped plot at the corner of Southwark Bridge Road and Southwark Street, backing on to the Peabody Southwark Street Estate.
The existing six-storey building is currently vacant but was previously used as a disaster recovery centre.
The proposed development will have an eight-storey element on Southwark Street and six-storey block on Southwark Bridge Road.
Ms Parry said that Southwark planners welcomed the "uplift in high quality employment floorspace," adding: "We believe that there is high standard of urban design and architecture, which is acceptable in townscape and heritage contexts."
The fate of the stone pediment - from the United Friendly Insurance Company headquarters that previously stood on the site - preserved on the Southwark Bridge Road side of the current block is unclear.
Neil Thompson from CLI Dartriver told councillors: "In economic terms the building can support almost 3 per cent of Southwark's 20-year jobs target, generating an additional £3 million of local spending annually."
Planning committee chair Cllr Richard Livingstone said he had "some reservations" about the development - including its impact on daylight and sunlight to residents of the Peabody Estate.
He added: "I do think it's not great having abandoned buildings in such a key location in the central business zone, and it would bring some life and some much-needed jobs."
The committee resolved unanimously to grant planning permission.