The preferred route of phase two running northwards from Birmingham will have five stops at: Manchester; Manchester Airport; Toton in the East Midlands; Sheffield; and Leeds, reports The BBC.
Chancellor George Osborne said it was “the engine for growth in the north and the midlands of this country”.
Phase one’s London-Birmingham link has faced considerable opposition.
Critics dispute the economic case, arguing that it ignores passengers’ ability to work on trains, and suggest swathes of picturesque countryside will be blighted by the railway.
Mr Osborne’s Tatton constituency in Cheshire is among the places that phase two of the route will pass through.
The chancellor said: “As a country you have got to make those long-term choices.
“If our predecessors hadn’t decided to build the railways in the Victorian times, or the motorways in the middle part of the 20th Century, then we wouldn’t have those things today.
“You have got to commit to these projects even though they take many years.”
The Department for Transport said that HS2 phase two would virtually halve journey times between Birmingham and Manchester – to 41 minutes – and between London and Manchester from two hours and eight minutes to one hour and eight minutes.
Speeds of up to 250mph on HS2 will also reduce a Birmingham to Leeds journey from two hours to 57 minutes, while phase one will cut London-Birmingham travel to 49 minutes, from the current one hour and 24 minutes.
Transport Secretary Patrick McLoughlin said: “It’s not just about journey times, it is also about capacity.
“We are finding the railways are overcrowded. We’ve seen massive growth in rail passenger numbers, so this is taking HS2 so it serves the north.”
He added: “This is the first railway to be built north of London for 120 years.”
Leeds City Council leader Keith Wakefield said: “We have lobbied long and hard for a high-speed rail link to Leeds and this is excellent news.
“It will strengthen Leeds’ position as the northern transport hub and unlock major investment, jobs opportunities and connectivity to the rest of the country.”
A final route for phase two is expected to be chosen by the end of 2014.
A proposed spur to Heathrow Airport has been put on hold pending a review of UK aviation policy, due to report in 2015.