The brothers plan to demolish the existing building – formerly offices of Tate & Lyle on the Thames – to build 165 luxury flats.
Foster and Partners designed the 280,000 sq ft scheme across a part nine-storey, part 11-storey building development.
The site was bought for £34m from administrators KPMG earlier this year, marking CPC’s first property acquisition since its ill-fated Chelsea Barracks purchase four years ago for £959m with backing from Qatari Diar.
A spokesman for CPC said: “The redevelopment seeks to address the potential of this part of the North Bank of the River Thames as a residential scheme, enhancing the vitality and character of the area whilst delivering an exceptional living experience in a prominent location in the City of London.
“London architects Foster + Partners have been working with CPC Group on the redevelopment proposals following their appointment in July 2012. Close consultation with the City Planning Department, GLA and other stakeholders has also taken place.”