Construction of the 240,000 sq ft building, which will offer opening windows, on-floor terraces and a roof terrace, is now to start this summer.
Galliford Try and Ardmore construction are believed to be among the bidders chasing the project.
Architect EPR and M&E consultant Sweco designed the project to target a BREEAM Outstanding rating.
Tristram Gethin, Founding Partner at Quadrant, said: “Receiving consent for Plot A is a huge step forward for this site and is exciting for us and the Nine Elms community.
“The space we’ll create here will be well suited to post-pandemic occupiers, with a focus on collaboration, wellness, sustainability and quality.
“With the US Embassy and Apple creating a new campus close by, we expect strong demand for office space in Nine Elms. The considered design we have developed is aimed at accommodating the wide variety of occupiers seeking out offices that nurture innovation and creativity.”