The contract between TfL and Bombardier covers the supply, delivery and maintenance of 65 new trains and a depot at Old Oak Common.
The contract award is subject to a 10 day standstill period.
TfL will run Crossrail as part of its integrated transport services for London, including ticketing and customer travel information.
Bombardier has confirmed that the new trains will be manufactured and assembled at their plant in Derby.
This contract will support 760 UK manufacturing jobs plus 80 apprenticeships.
An estimated 74 per cent of contract spend will remain in the UK economy.
The construction of the maintenance depot at Old Oak Common will see 244 jobs, plus 16 apprenticeships.
When fully operational the depot will support 80 jobs to maintain the new fleet of trains.
Mayor of London, Boris Johnson, said:
'The Crossrail project is now rolling on full-steam ahead.
'The manufacture of these new trains will not only revolutionise rail travel in London, they will deliver jobs and economic growth in their birthplace in Derby and across the UK.
'With a firm on board to deliver a fleet of 21st Century trains and the tunnelling more than halfway complete, we're on track to deliver a truly world-class railway for the capital.'
Transport Secretary Patrick McLoughlin said:
'This announcement will mean state of the art trains providing quick, comfortable journeys for the millions of people Crossrail will serve.
'It is also great news for British manufacturing and for Derbyshire, where Bombardier will support 760 new jobs and 80 apprenticeships.'
Sir Peter Hendy CBE, London's Transport Commissioner, said:
'Crossrail is already generating jobs in London and the UK.
'When it opens it will continue to provide jobs and the growth it will bring will boost the whole economy.
'Crossrail is a fantastic example of the widespread benefits that sustained investment in transport infrastructure brings.'
Andrew Wolstenholme, Chief Executive of Crossrail, said:
'Crossrail will transform rail services in London and the South East.
'Procurement of the rolling stock and depot is just one more step in delivering this new railway and making it a reality for millions of passengers.
'Crossrail Limited has conducted this procurement in a fair, objective and transparent manner and in full compliance with the regulatory framework.'
London's population is set to grow from 8.4 million today to around 10 million by 2030.
Government, the Mayor of London and Transport for London are investing in Crossrail and other transport infrastructure to support access to jobs, education, housing and to boost economic growth.
Crossrail will boost London's rail-based capacity by 10 per cent connecting Maidenhead and Heathrow in the west and Shenfield and Abbey Wood in the east.
It is connecting people and places, providing faster journey times and up to 24 trains per hour between Paddington and Whitechapel during the peak.
In addition to the jobs created through the rolling stock and depot contract it is estimated that Crossrail will generate at least 75,000 business opportunities and support the equivalent of 55,000 full time jobs right around the UK.
Three out of five businesses currently winning work on the project are based outside London and over half are small and medium-size companies (SMEs).
Each Crossrail train is 200 metres long and able to carry up to 1,500 passengers.
Key features of the new high-capacity Crossrail trains include air conditioning and inter-connecting walk-through carriages.
On-train passenger information systems will deliver real-time travel information to allow passengers to plan their onward journeys.
The new lightweight Crossrail trains will be built with an emphasis on energy efficiency and use of intelligent on-train energy management systems.
All bidders were asked to set out how they would engage with their wider supply chains and maximise opportunities for SMEs.
Bombardier will target at least 25 per cent of the value of this contract going to SMEs.
Bidders were required to manage the project through a London-based office, and to commit to have plans to deliver job and training opportunities, including apprenticeships.
TfL will introduce the new trains from May 2017, with the fleet progressively introduced to the existing rail network well in advance of services commencing through Crossrail's central section in December 2018.
Welcoming the announcement TUC General Secretary Frances O'Grady said:
"This is wonderful news for Derby, the East Midlands and UK manufacturing. Workers in the city will be relieved to learn that jobs and apprenticeships at the factory have been secured for a good few years.
"It's down in no small part to the Bombardier management and workforce who have worked hard to keep the business alive – a campaign which was strongly backed by local people and unions in the region from the very beginning.
"Ministers clearly listened to union concerns and made sure that any firms who wanted to win the contract had to show how they would put taxpayers' money to good use and invest in jobs and the local economy."