The £40m job will see the JV provide all works associated with the construction and fit out of the intermediate shafts and headhouses at Eleanor Street and Mile End Park
The shafts will provide access for ventilation, maintenance intervention, emergency exit and emergency services access for the main railway.
Work will start this month and is expected to complete in August 2018.
Andrew Wyllie, Chief Executive of Costain, said: “This contract award is as a result of the successful implementation of our ‘Choosing Costain’ strategy, in which we focus on winning repeat business with major blue chip customers who are spending and will continue to spend on large scale projects.
“This is our fifth contract with Crossrail and further contributes to the strength of our order book, of which 90% is repeat business.”