The firm is believed to have beaten off fierce competition for the £10m job from Coinford Construction and CJ O’Shea.
Work on Phase 2 of Academy Central on the former University of East London campus will start next month.
A further five phases are planned on the scheme which will involve construction of 936 homes in total over the next seven years.
The award is the latest win in a growing number of contracts let by house builders as the private market continues to show signs of recovery.
A site source told the Enquirer: “It was a keen contest between the three but Anderson won out.
“There is a lot of work in the pipeline in this region from Taylor Wimpey with big schemes like this and its Pulse development in Romford starting again.
“The mix on site is also changing with private housing coming to the fore whereas in the past most work was driven by social housing.”