In March, Stagecoach beat rival bids from Great North Eastern Railways and a joint venture of FirstGroup and Dutch Railways to win a 20-year franchise to run SWT.
The coaches will boost rush-hour capacity by 25% on South West Trains' (SWT) services between south-west and southern England and London Waterloo.
The order, Britain's biggest yet, has been placed with German company Siemens with financing by the Royal Bank of Scotland's Angel Trains.
It forms part of Stagecoach Group's commitment to a £1.7bn investment in new trains and infrastructure.
In March, Stagecoach beat rival bids from Great North Eastern Railways and a joint venture of FirstGroup and Dutch Railways to win a 20-year franchise to run SWT.
Stagecoach Group chief executive Keith Cochrane said new carriages were crucial to improvements promised for SWT.
"We at Stagecoach, together with our partners Siemens and Angel Trains, have signed this deal at the earliest possible opportunity as a first step to deliver a better service to our passengers in the new South West Trains franchise," he said.
The first of the carriages should enter service in November 2002, with the whole fleet available by September 2004.
They will replace the old Mark 1 slam-door trains, which must be phased out by the end of 2004.
The arrival of the new rolling stock will mean more-frequent services to London on the Windsor, Woking and Basingstoke lines.
Strategic Rail Authority chief executive Mike Grant said: "This deal ensures that passengers will benefit from new trains as soon as possible, with additional coaches to provide more capacity on busy commuter routes.
"It marks an important step towards our objectives of increasing rail use by 30% over the next 10 years and reducing overcrowding."
Siemens has said the carriages will be built in Germany.
New jobs
The deal, which includes maintenance, is expected to generate several hundred new jobs in project management, engineering and building new rolling stock maintenance facilities.
The chief executive of Siemens, Alan Wood, said: "We are delighted to be signing the biggest order that Siemens has received in over 150 years here in the UK.
"This win underpins our commitment to support the UK railway industry and the crucial role that new rolling stock will play in delivering a better service to the travelling public.
"We anticipate that passengers will see a marked improvement once our trains are operational."
One of the losing bidders for the order, Alstom said it was too early to say whether jobs will have to go among 2,000 workers in rolling stock factories in Birmingham and Preston.
Alstom is still in the bidding, along with Siemens and Adtranz, for an order, due to be placed in June, from the South Central franchise for up to 1,000 new carriages.
SWT ordered 120 coaches from Alstom two years ago - but only a handful have entered passenger service, because of reliability problems.