Details of the next phase of the £32bn HS2 high-speed rail network have been unveiled by the government.
The preferred route of phase two goes north from Birmingham along two branches, with new stations at Toton near Nottingham, Sheffield, Leeds, Manchester and Manchester Airport.
Prime Minister David Cameron said there were particular benefits to linking the UK's major cities with high-speed rail.
Phase one's London-Birmingham link has faced considerable opposition.
Critics argue that HS2's predicted economic benefits have been overestimated by the government, and suggest swathes of picturesque countryside will be blighted by the railway.
Chancellor George Osborne's Tatton constituency in Cheshire is among the places phase two will pass through.
But he said: "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."
Mr McLoughlin told MPs a period of informal consultation on the exact route would start immediately and inform an official public consultation later this year, with a firm decision reached in 2014.
A proposed spur to Heathrow Airport has been put on hold pending a review of UK aviation policy, due to report in 2015.
More than 70 groups oppose HS2. StopHS2 argues the project is "fundamentally flawed", saying the majority of journeys will be to London so England's North and Midlands will lose out rather than benefit, and that projections do not take into account competition from conventional rail.
StopHS2 campaign manager Joe Rukin said: "Fifty-five percent of the economic benefits are based on the cash value of time, no-one works on trains and every business user is worth £70,000 a year - it's basically a train for the rich that everyone else is not only going to have to pay for the construction of but also have to subsidise throughout its lifetime as well."
Other opponents object on the grounds that HS2 will cut through picturesque countryside, and 18 councils along the route have said taxpayers cannot afford the line, and that it will increase greenhouse gas emissions.
The phase two announcement was welcomed by officials in northern English cities including Leeds, where city council leader Keith Wakefield said: "It will strengthen Leeds' position as the northern transport hub, and unlock major investment, jobs opportunities and connectivity to the rest of the country."
Deputy Prime Minister Nick Clegg said: "We can't keep turning a blind eye to the north-south divide in our economy. That is what this high-speed project is all about."
Construction on the Y-shaped extension could start in the middle of the next decade, with the line open by 2032-33.
While new stations will be built at Manchester Airport, Manchester, Leeds, Sheffield and Toton, high-speed trains will also stop at Crewe's existing station on their way to Preston and Liverpool.
They will also be able to continue to Runcorn, Wigan, Durham, Newcastle, Glasgow and Edinburgh.
Construction of the London-West Midlands route is expected to begin around 2017, once Parliament has approved the necessary powers, probably in 2015.
The Toton station along phase two of the route will primarily serve Derby and Nottingham, while the Sheffield station will be sited at the Meadowhall shopping centre five miles from the city centre.
Labour's shadow transport secretary Maria Eagle said: "I think it's tremendously important that we link our airports to our cities, not some station in the middle of nowhere near a city and bypass our main hub airports.
"So I think there are questions to be asked and we will be asking them, but overall this is a good thing for the country and we need to get on and give certainty."
She previously highlighted "worrying signs that the Department for Transport's timetable to deliver this vital infrastructure is slipping".
Details have also been published of the consultation on HS2 Ltd's proposed exceptional hardship scheme for phase two, which will cover compensation to affected property-owners.