The legislation releases funds to pay for surveys, buy property and compensate evicted residents.
The Prime Minister welcomed the vote hailing HS2 as an absolutely vital programme.
It came as the Government today announced it would carry out a new study into the gains from extending HS2 to Scotland.
David Cameron said: “I’m absolutely sure it’s an essential piece of work for the country. It’s not just about journey times, it’s about capacity.”
He added that he hoped Labour would see sense and stop talking about pulling the plug on HS2 and get behind it.
MPs backed the paving bill by 350 votes to just 34 in its final reading in the House of Commons.
Among those voting against the bill at its third reading stage were 17 Conservatives and 11 Labour MPs.
The proposed legislation will now go to the House of Lords for final scrutiny.
Government has been battling with critics of the scheme since it revised the estimated cost of building the high-speed link between London and the North of England from £32.7bn to £42.6bn this summer.
Despite concerns about soaring costs, The Government today announced it had instructed HS2 Ltd to identify ways to make further rail capacity and journey time improvements between northern England and Scotland for both passengers and freight.
This will include looking to cut journeys from Glasgow and Edinburgh to London to 3 hours or less.
UK government Transport Minister Baroness Kramer said: “Our goal for HS2 is for a truly national network that will bring the UK and its cities closer together. We are driving forward HS2 because the benefits it will bring are huge.
“Without it we face a crisis in capacity on our rail network. But it is also about connectivity, across the UK 18 cities including Glasgow and Edinburgh will be better connected because of HS2.”
HS2 Ltd, working with the Department for Transport, Scotland Office, Network Rail and Transport Scotland will generate a list of options.
Improvements could include extending high speed lines, making upgrades to existing lines, or a combination of the 2.
A final report will be submitted to the Department for Transport next year for ministers to consider.
