It will run from Crewe to Manchester and connect the West Midlands to Leeds.
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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.
A final decision on the £56billion project is not expected until next year.
It's hoped the high-speed line will boost the economy by billions of pounds.
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, taking the high-speed line to north-east and north-west England and beyond, is due to be completed by around 2032/33.
Passengers travelling on the East Coast and West Coast main lines will benefit from more services and extra seats once the HS2 high-speed rail project is completed, the Department for Transport (DfT) has said.
The number of seats could treble to around 15,000, according to the DfT.
The department acknowledged that many intercity services are currently "full to overflowing" but said that with HS2 they "will not be so crowded".
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."
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."
The Government originally set out plans for HS2 Phase Two in 2013. Since then it was decided to develop Phase Two in 2 stages:
Phase 2a – from the West Midlands to Crewe that was announced last year
Phase 2b – from Crewe to Manchester and from the West Midlands to Leeds, South Yorkshire and the East Midlands
Phase 2a will open in 2027, Phase 2b in 2033.