But Transport Secretary Justine Greening will face a battle to get her plans through, as opponents of the project plan to fight on in their efforts to derail it.
Aware of the strength of feeling of the anti-lobby, Ms Greening did announce that more of the £16.4 billion London-Birmingham first phase of the project - which passes through picturesque Tory heartlands - would be in tunnels.
She also announced extra measures to assist those affected by the scheme that will, by 2026, see 400 metre-long trains capable of holding 1,100 passengers, whisking them on a 140-mile route from London to Birmingham in just 45 minutes.
She said the scheme, which will include a second phase to Manchester and Leeds by 2033, would mean more seats, better connections, new jobs, and growth and prosperity for the entire country.
"HS2 will link some of our greatest cities - and high-speed trains will connect with our existing railway lines to provide seamless journeys to destinations far beyond it. This is a truly British network that will serve far more than the cities directly on the line," she said.
But those opposed said the project was a "white elephant", there was no business or economic case for it and no money to pay for it.
The Government's own figures showed that because of the economic climate, the benefit-cost ratio of the project (including wider economic benefits) had reduced slightly - to between £1.80 to £2.50 benefits for every £1 spent - although the figure still remained "convincing".
A hybrid Bill will be introduced in Parliament next year for the London-Birmingham phase which will start at a rebuilt Euston station in London and finish at a new Birmingham City Centre station on Curzon Street.
There would be a Crossrail interchange station at Old Oak Common in west London and a second interchange station to the south-east of Birmingham.
A direct link to HS1 (the London to Folkestone Channel Tunnel high-speed rail line) will be built in phase 1, but a spur linking to Heathrow airport would not be built until the second, north-of-Birmingham phase of the project.
The second phase will see lines built from Birmingham to Leeds and Manchester by 2033. A formal consultation on second phase routes will begin in early 2014 with a final route chosen by the end of 2014.
HS2 will mean substantial time savings between Britain's cities, reducing a Birmingham to Leeds journey from two hours to just 57 minutes and a Manchester to London journey from two hours eight minutes to only one hour eight minutes.
Some Tory MPs, including Welsh Secretary Cheryl Gillan, as well as local residents and some councils are bitterly opposed to HS2.
Changes Ms Greening has made to the route include a longer, continuous tunnel from Little Missenden to the M25 through the Chilterns and a new 2.75-mile bored tunnel in the Ruislip area of north-west London.
The changes also mean that fewer properties will be affected by extra, or high levels of, noise.
Asked why changes had been made to the HS2 scheme, Prime Minister David Cameron's official spokesman said: "We had a consultation and within that consultation some people expressed concerns and we have listened to those concerns."
Mr Cameron has not had any meetings with Ms Gillan recently specifically to discuss her concerns about the plans, he said.
The spokesman added: "The point of this scheme is that for every pound spent, it generates £2 in benefits. This is vital to our efforts to rebalance the economy and tackle the problem of the north/south divide."
The announcement and the changes to the route failed to appease Andy Jones, 60, whose home in Burton Green, Warwickshire, is about 90 yards from the proposed route.
He said his village regarded the announcement as being "day one of round two" in the fight against the line.
He added: "The consultation was an utter sham from start to finish."
Ms Greening said: "HS2 will link some of our greatest cities - and high-speed trains will connect with our existing railway lines to provide seamless journeys to destinations far beyond it. This is a truly British network that will serve far more than the cities directly on the line."
She said it was not a decision she had taken lightly "or without great consideration of the impact on those who are affected by the route from London to Birmingham."
Ms Greening said the changes meant that more than half the London to Birmingham route would be out of sight in tunnels or cuttings.
Network Rail and the Association of Train Operating Companies welcomed the announcement, with both organisations reckoning that expanding existing rail routes was not enough to combat overcrowding.
Rail unions were also pleased with the go-ahead for the scheme.
But the Taxpayers' Alliance and the Stop HS2 campaign both said the project was "a white elephant", while the Institute of Economic Affairs said the scheme was "economically flawed".
Jerry Marshall, chairman of Agahst (Action Groups Against High Speed Two), said HS2 was "a disaster waiting to happen", but the British Chamber of Commerce said rail services would get worse without the new line and the CBI said the announcement was welcome.
And Stop HS2's campaign co-ordinator, Joe Rukin, claimed the route was simply the "wrong priority" for the country.
Mr Rukin, from Kenilworth in Warwickshire, said: "There is no business case, no environmental case and there is no money to pay for it."
PA
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