Although the blocks, which will range in height from seven to 13 storeys, will have concrete cores, the rest of the buildings will be made almost entirely from timber.
Other than minimised concrete reinforcement, no other steel will be used in the development, which replaces an earlier scheme - by another practice - turned down by planners.
A spokesman for dRMM said: 'The joint ambition is to produce a high-rise that is structurally and environmentally groundbreaking for a society which values architecture and nature.
'The towers, [are] designed with a minimal footprint - supported by a double-height structural trunk which allows optimal views from the communal landscape.'
The scheme is scheduled to start on site next year.