The contract award follows on from a pre-construction development agreement signed in June 2017.
After securing a detailed planning consent, Henderson Park and Greystar have now completed the purchase of the land from Royal Mail Group for £101m.
The phased development is expected to be completed in late 2024 and will be within walking distance of two new London Underground stations on the extended Northern Line, on the south side of the River Thames.
The contract sum is £276.4m, with monthly payments to be made in accordance with work undertaken and a final payment on completion.
Telford Homes chief executive Jon Di-Stefano said: "We are delighted to be building this exciting scheme for Henderson Park and Greystar. We have been working on the detailed design for some time such that we can immediately start work on site. We continue to make progress against our objective to increase the group's output of build-to-rent homes in London, and this contract with Henderson Park and Greystar, with whom we have a strong relationship, highlights our position as a trusted partner at the forefront of this fast growing sector."