Students will have to pay tuition fees of up to £3,000 a year under plans confirmed by the government.
Universities are being freed to increase tuition fees from the present level of £1,100 a year, but students will not have to pay until after they graduate.
For the first time different universities will be able to charge different fees up to £3,000.
The plans are part of a wide-ranging and long-awaited shake-up of higher education in England.
Students are warning they will graduate with debts of up to £30,000 and that the changes will lead to an elitist system.
But they are pleased with one of the new measures - the re-introduction of maintenance grants for the poorest students, which were scrapped by Labour in 1998.
The changes were announced by Education Secretary Charles Clarke in the Commons.
HIGHER EDUCATION REVIEW
Higher limit for tuition fees, up to £3,000
Universities set own fees
Scrapping of up-front fees
Re-payment after graduation
'Access regulator' to ensure wider intake
Return of maintenance grants
He said the whole package was "good news" for universities and a "massive step forward".
The government has already said students who go to university under the new arrangements could leave with average debts of about £15,000.
Mr Clarke said the government had to act: "This House needs to acknowledge that coasting along, basking in previous success and shirking the need for
reform offers no robust future for our universities."
The shadow education secretary Damian Green said rows within the Cabinet had led to "messy, botched"
proposals which would satisfy no one.
And the Liberal Democrats' education spokesman Phil Willis said: "Burdening students with
£20,000 of debt won't increase the chances of our poorest young people going to
"Britain's universities will become a two-tier education system, with
universities separated by what they can charge and students split by what they
Mr Clarke's predecessor, Estelle Morris, described the plans as "his baby, not mine".
Speaking after receiving an honorary doctorate from the University of Warwick, Ms Morris said only people who could afford to would go into higher education.
The increase in fees is intended to tackle the budget shortfalls facing many universities and help pay for the expansion the government wants.
Ministers want at least half of young people to enter higher education by 2010.
The plans give the sector an annual increase in funding of 6% a year for the next three years.
Mr Clarke announced there would be an Access Regulator who would check that any university which wanted to increase its tuition fees had admissions procedures that encouraged applications from students from less advantaged families.
Back bench opposition
Since it was announced in 2001, the higher education review has been a political battleground.
The issue is reported to have split the cabinet and Labour backbenchers have been unhappy at the prospect of students facing large debts.
Immediately after announcing his plans to the Commons at lunchtime, Mr Clarke went to meet Labour MPs to try to win them over.
Labour MP Lynne Jones was one of the 180 Labour and opposition backbenchers who signed a Commons motion against top-up fees.
"It is quite frankly laughable to suggest that the creation of an access regulator is going to be sufficient to counter-balance the disincentive effect of these massive state-organised debts that students are going to
encounter," she said.
Students have argued that allowing universities to charge different levels of fees will mean that applications will depend on ability to pay rather than ability to learn.
They warn students could be left with debts of up to £30,000, with medical students getting even further into debt.
Mandy Telford, president of the National Union of Students, said: "The student funding review was called in order to address the balance of contribution between the student and the state.
"That balance has certainly been addressed today with students footing the bill."
Elsewhere in the UK
The main thrust of the proposals will be for England.
Charles Clarke has confirmed he is to hold further talks with the Welsh Assembly on handing it power over student funding and tuition fees.
In Scotland up-front tuition fees were never introduced for Scottish students, and ministers have made it clear they are against top-up fees.
There are fears of an influx of English "fee refugees".
An urgent summit has been called to examine what the impact of the White Paper might be.
Northern Ireland's two universities say they are "in limbo". They are funded through the English higher education funding council.
The education minister, Jane Kennedy, said the government had not ruled out implementing its proposals in Northern Ireland too.