This will enable the route to link with Heathrow airport in west London.
Transport minister Lord Adonis said: "Crossrail is the largest addition to the transport network in 50 years, and the announcement represents a major step towards its delivery. Business has long been a strong advocate for Crossrail and this is borne out today."
The contribution, however, is subject to the approval of the Civil Aviation Authority - BAA's economic regulator.
In return for the injection, Crossrail will guarantee a fast train service four times an hour for the majority of the day.
This will provide direct services from Heathrow airport through central London, the City and Canary Wharf and out to Shenfield and Abbey Wood.
BAA's strategy director Mike Forster said: "We are delighted to support the Crossrail scheme, which demonstrates our commitment to improving public transport access to Heathrow."
Mayor of London Boris Johnson added: "The agreement with BAA is very welcome news and underlines the commitment that businesses, as well as Transport for London and the Government, are showing towards delivering the funding package for Crossrail.
"This is another significant step forward in preparing for the construction of this landmark new railway. Works have already begun at Tottenham Court Road station and the contracts to design and build the multi-billion pound project are all on track to be awarded by spring 2009. All parties are committed to Crossrail's success, and together we will deliver it on time and on budget."
After years of delay and following a scrapping of the scheme in the 1990s by the Conservatives on cost grounds, Crossrail was finally given the go ahead by Prime Minister Gordon Brown days before what everyone expected would be the announcement of a general election in autumn 2007.
The scheme is expected to be complete in 2017.