The first train has travelled on the high-speed Channel Tunnel Rail Link (CTRL) through Kent.
The first passenger services will run at the end of September
The £1.9bn, 46-mile first half of the line, was opened on Tuesday with a ceremony at Waterloo station.
Prime Minister Tony Blair said the completion of first part of the CTRL should give the UK "some optimism and some spur" for similar projects in the future.
The new section of line will cut journey times from London to Paris and Brussels by 20 minutes.
The first passenger service to take advantage of the line and its reduced journey times will run on 28 September.
The £1.9bn, 46-mile first section runs from the tunnel near Folkestone, to Fawkham Junction in north Kent.
NEWER FASTER TIMES
London-Paris: 2hr 35min
London-Brussels 2hr 20min
London-Lille: 1hr 40min
The gentle curves and gradients and computerised signalling mean Eurostar trains on the line will finally be able to reach their full operating speeds - 186mph.
Mr Blair accepted a certificate which allows services to run on the CTRL and said its completion on time and on budget was "a great omen" for the future.
He said: "The imagination and vision that has created this project should give us some optimism and also some spur as to what we could do in the future.
"The truth is we need to renovate a large part of our transport infrastructure in this country and we have shown through the Channel Tunnel Rail Link...that it can happen."
Officials from rail firms on both sides of the Channel were among the crowd of about 100 VIPs he addressed at the London station.
Many of them then boarded a specially-chartered Eurostar train to Sandling in Kent, where further celebrations were due to take place.
Earlier, Eurostar spokesman Paul Charles told BBC Radio 4's Today programme: "This is a great day for the UK rail industry.
"It is a new era, with high-speed lines opening in the UK for the first time.
"This is the start. It could clearly be a blueprint for other lines in the future."
The £3.3bn second half of the link will run from north Kent to St Pancras, and is due to be completed in time for passenger services to start in 2007.
When the 68-mile link is completed and runs all the way from London to the coast, the London-Paris time will be two hours 15 minutes and London-Brussels two hours.
The link will also provide the infrastructure for high-speed commuter services from Kent to London.
Tony Blair called the opening of the first half of the line "a great omen"
Many cross-Channel commuters will be relieved at the end to the "national embarrassment" of trains slowing sharply as they cross from France to England.
It is nine years since the UK's high speed route to the Channel was first decided, and 10 years since France completed its version.
Transport Secretary Alistair Darling agreed the link would provide "a valuable contribution to Britain's railway".
He told Today: "My objective is to make sure that we have a railway system that supports this country and enables people to get around."
He said the link would make a big difference to Eurostar's ability to compete in the transport market against airlines flying to Brussels and Paris.
"It will demonstrate that if you put some money into the railways and manage them properly, you can get a lot more out of them," he said.