O’Rourke fought-off competition from Costain, Geoffrey Osborne and Hochtief to land the job to build the above ground station.
The win completes a Crossrail hat-trick for O’Rourke after the firm won the main £300m Liverpool Street Station contract and the £200m Tottenham Court Road station job earlier this year.
Work on the Custom House C520 contract is due to start early next year and be finished by 2018.
The new station will include a new ticket hall, interchange with Docklands Light Railway and step-free access between the street and Crossrail platforms