Under the terms of the surprise pounds 140m deal, which is subject to official approval, Stagecoach proposes to take a 49 per cent stake in Virgin Rail.
The tie-up leaves Mr Branson, who originally had a 41 per cent stake, with control of his rail subsidiary with a 51 per cent share.
Stagecoach is offering to buy out four venture capital backers of Virgin, who will see huge profits on their original pounds 45m investment two years ago.
However, the Government made it clear it planned to wring extra benefits for rail passenger from the tie-up.
Ministers are keen to extract more for the traveller. They point out that Virgin Rail received more than pounds 170m in subsidy this year from the public purse and has promised much - including more than 130 new trains - but little has so far materialised.
John Prescott, the Deputy Prime Minister, is keen to integrate more bus and coach services into the rail network and has plans for a profit-sharing deal with rail companies.
Mr Souter said the deal would mean a "more integrated approach".
"North of Edinburgh and Glasgow the road system is much better than the rail system and we could see Virgin branded coaches dropping people off at stations to catch trains. For example, Hamilton is on the M74 and we could have a bus service linking it there."
"What we're looking at in the future is actually feeding in Stagecoach bus services in the North-west into our stations in Manchester and elsewhere," he said.
"It's been a bugbear of many critics in the past that simple things like timetabling and ticketing are not integrated as well as they should be."
Virgin Rail, which comprises the West Coast service and the CrossCountry franchise, is a sprawling network which links every major city in Britain. Although it has recently had a poor service record - which saw more than one in five trains delayed - Virgin Rail made a profit of nearly pounds 13m in the 11 months up to March this year.
Virgin intends to bring in 54 tilting trains on the London to Scotland West Coast route and is introducing tilting and non-tilting new diesels on CrossCountry. The pounds 2.1bn package also involves Railtrack, the owner of the nation's track and signalling. There will be an overhaul of the West Coast main line reducing London to Glasgow journey times from five hours to three hours 49 minutes by summer 2005.
Signed at 4am yesterday, the deal means that Mr Branson will not return in the near future to the stock market - which he left a decade ago.
Some analysts had questioned how easy it would have been to float a rail company - saying that recent failures such as Eurostar's aborted stock- market listing would have put off investors.
Stagecoach, which lost out to Mr Branson's rail team when British Rail was broken up, were lured to the deal when it examined Virgin's spectacular financial success. West Coast services carry 12 per cent more passengers than last year.
Mr Souter's company made its name operating coach services, already runs two rail lines - Island Line, the Isle of Wight route, and South West Trains, on which passengers experienced cancellations over a driver shortage early in 1997. The new partnership is subject to approval by Rail Regulator John Swift and by the Office of Passenger Rail Franchising.