Developer Hutchison Whampoa, in joint venture with Taylor Wimpey, is understood to have hired the Irish construction group to start building work at the Lots Road site on the bank of the Thames.
A start to building work draws to a close years of wrangling over the controversial £500m scheme, which straddled Kensington & Chelsea and Hammersmith & Fulham planning authorities.
The deal will mark another significant victory for P Elliott in the London construction market after landing a £35m-plus contract for plot 9 at the 2012 London Olympics athletes village.
Joint venture development company Circadian aims to build 800 homes across 13 buildings, including two towering 37 and 25-storey apartment blocks.
The scheme includes converting the disused Lots Road power station into a unique mixed-use development, the two remaining chimneys modified to house public viewing galleries offering sweeping views of the Thames and London.
After years of argument, the Terry Farrell designed scheme won planning approval last October, and several firms have been bidding to build the first of the towers expected to be cost around £45m.
P Elliott was among the hopefuls after a slice of the action on this or subsequent phases of the housing project.
Balfour Beatty, Laing O’Rourke, Sir Robert McAlpine, Sisk and Vinci have also priced works.