The Government has set out its preferred route for the northern section of HS2.
Phase 2 of the high speed rail project will see the line run from Crewe to Manchester and the West Midlands to Leeds.
The plan does not include a new station in Sheffield, after proposals to run trains to the Meadowhall shopping centre were shelved.
Ministers have suggested that HS2 should serve the existing Sheffield city centre station, but critics have warned this would mean a new housing estate in nearby Mexborough would face demolition.
The Government has claimed that passengers travelling on the East Coast and West Coast main lines will benefit from more services and extra seats once HS2 is up and running although the current estimate for completion of all of phase 2 is not until 2033.
Phase 1 of the £55.7 billion HS2 railway is due to open in December 2026 and will see trains travel at high speed between London and Birmingham before running on from Birmingham on the existing West Coast Main Line.
A second Y-shaped phase will open in two stages. Phase 2a from the West Midlands to Crewe will launch in 2027 and phase 2b, from Crewe to Manchester and from the West Midlands to Leeds, South Yorkshire and the East Midlands, will open in 2033.
Transport Secretary Chris Grayling said: "Our railways owe much to the Victorian engineers who pioneered them, but we cannot rest on their legacy when we face overcrowding and capacity problems.
"HS2 is an ambitious and exciting project and the Government is seizing the opportunity it offers to build a transport network fit for the 21st century, one that works for all and makes clear to the world that Britain remains open for business.
"The full HS2 route will be a game-changer for the country that will slash journey times and perhaps most importantly give rail passengers on the existing network thousands of extra seats every day. They represent the greatest upgrade to our railway in living memory.
"But while it will bring significant benefits, I recognise the difficulties faced by communities along the route. They will be treated with fairness, compassion and respect and, as with Phase 1, we intend to introduce further compensation which goes over and above what is required by law."
Former Chancellor George Osborne said he "strongly" welcomed the Government's "renewed commitment" to the second phase of HS2.
He added: "Now let's commit to HS3, the high-speed rail link across the Pennines, so we have a coherent plan to speed journeys across the North.
"We need certainty about the route and effective compensation to help communities directly affected by HS2, including those in my Cheshire constituency.
"Hinkley, Heathrow and HS2/HS3 are the three projects we spent years laying the groundwork for. Time for talking over; now time for delivery."