The deal must await a 10-day standstill period before it is final, Bombardier Transportation, based in Berlin, said in a statement on its website.
"We are absolutely delighted to have been recommended as the winning bidder for the Crossrail rolling stock and depot contract and look forward to closing the contract with the customer," Francis Paonessa, managing director for Bombardier Transportation UK, said.
Bombardier called it "a resounding endorsement" of its proposed Aventra train.
London's Daily Telegraph said the contract with the Department of Transport and Transport for London is valued at $1.6 billion and will support more than 1,000 jobs in Britain.
The government said Bombardier will build the trains at its plant in Derby, England, keeping 760 manufacturing jobs and 80 apprenticeships positions going. Building the maintenance depot at Old Oak Common will support 244 jobs and 16 apprenticeships during construction and 80 permanent jobs maintaining the new trains, the Telegraph said.