The £50m project will see the joint venture shift around 4.5 million tonnes of excavated materials to be used to create a RSPB nature reserve.
The specialist marine joint venture beat rival bids from Carillion, a Cemex /Keltbray joint venture, Lagan Construction, Port of Sheerness and VolkerFitzpatrick.
Andy Mitchell, Crossrail programme director said: “At least two-thirds of all Crossrail excavated material will be used to create the wetland at Wallasea Island.
“With the award of the contract to transport excavated material, Crossrail has now awarded the last remaining major contract that will allow tunnelling to commence in spring 2012.”
Crossrail tunnelling will commence at Royal Oak in March with the first ships containing the excavated material arriving at Wallasea Island during summer 2012.
The contractor will be responsible for shipping excavated material from Instone Wharf and Barking Riverside in east London and Northfleet, Kent to Wallasea Island.
Up to five ships a day will transport excavated material down the River Thames to Southend–on-Sea.
They will then travel north passing Foulness Island before turning west into the River Crouch to reach Wallasea Island.
Contract C806 to construct the jetty at Wallasea Island was awarded to BAM Nuttall earlier this year.
Construction of the new jetty is currently underway and will complete next year.