The Rail Franchising Office said Virgin was the preferred bidder for the CrossCountrytrain company.
A formal announcement that Virgin has officially won the franchise is expected to be made soon.
A spokesman for Virgin, Will Whitehorn, said: "We are very excited.
"We think this is a major national network with huge potential."
Virgin is a partner in London & Continental Railways, which has taken over the running of the high-speed Channel tunnel Eurostar train service and which will build the pounds 3bn Channel tunnel high-speed rail link.
The success with CrossCountry is some consolation for Mr Branson, who had hitherto failed in bids to run privatised lines. In particular, he had high hopes of running the Gatwick Express route, only to lose out to bus company National Express.
From its headquarters in Birmingham, CrossCountry operates services as far north as Aberdeen, as far south-west as Penzance in Cornwall and as far south as Brighton.
Some of the service involves InterCity trains, while other services are of a long-distance nature, including a Penzance-Dundee service covering more than 700 miles and a Bournemouth-Glasgow service covering 470 miles.
Big city stations served by CrossCountry include Cardiff, Liverpool, Manchester, Glasgow and Paddington in London.
The company's passenger revenue in 1994-95 was pounds 102m and it employs about 840 staff.
Thirteen of the 25 train companies have now passed into private hands and all the remaining ones have been offered for sale.
The Government is hopeful of completing the entire privatisation of passenger services before the general election.