The contract to construct the Stratford tunnel portal at Pudding Mill Lane is thought to be worth around £15m.
The deal mirrors the joint venture’s Paddington package award in March to build the western tunnel portal at Royal Oak in London.
These two jobs are the first tunnel-related contracts to start on the £15.9bn project.
Pudding Mill Lane Portal, which is close to Stratford and adjacent to the existing DLR, will act as the transition ramp for Crossrail trains when entering and exiting the north east section of the central London tunnels.
Work will begin immediately and is scheduled for completion in summer 2011.
Andrew Wyllie, chief executive of Costain, said: “To have secured another contract on Crossrail so soon after the Royal Oak contract is excellent news.
“Crossrail will be one of the greatest engineering projects seen in the UK for some time and we are delighted to be playing a major early role in its delivery.”