The 12 Hammersmith Grove project will provide 167,000 sq ft of office space over 11 floors and is to be built speculatively.
Construction will start this May on the project, which is expected to cost £40m to build.
Wates built the first phase and is expected to be in line for the second phase, although Development Securities has not yet confirmed, which builder it will use.
Developed on the site of a former car park, 10 and 12 Hammersmith Grove are a significant new commercial and leisure destination in the centre of Hammersmith adjacent to the underground station.
The first phase of the development, 10 Hammersmith Grove, was completed last July.
Julian Barwick, Development Securities, said: “We are delighted to be progressing 12 Hammersmith Grove in partnership with SWIP Property Trust with whom we also developed 10 Hammersmith Grove.
“The appetite for premium office space in locations such as Hammersmith, on the edge of London’s traditional office core, is growing, as occupiers are increasingly price sensitive and yet still discerning with regards to quality.”