The Government made the concession as its controversial higher education Bill cleared its final hurdle in Parliament and was granted Royal Assent.
The Bill allows universities to charge fees of up to pound;3,000-a-year from 2006, which students will pay back after graduation when their salaries reach a certain point.
It also creates an Office for Fair Access, which will scrutinise the work that universities do with schools and other organisations to encourage students from under-represented groups.
Peers had demanded that students who finished school in 2005, but wanted to start university a year later, should be allowed to pay the current tuition fees of around pound;1,200.
The Lords argued that pupils who missed out on the A-level grades they needed would feel cheated and that students might abandon gap years to gain the cheaper fees.
The amendment was accepted by the Government, although it rejected other amendments by peers including one that said students should pay fees only for three years.
Charles Clarke, the Education Secretary, said there had been a constructive dialogue during the Bill's passage through the Lords.
"Everyone with potential should be given the opportunity and encouraged to aim high and go to university," he said.
"Higher education will now be free at the point of entrance and fair at the point of repayment - a fair and affordable option for students from all backgrounds."
Fears that greater fees might deter young people from lower-paid public-sector jobs such as teaching has led the Government to commission a report into public-sector recruitment.
Sir Alan Langlands, principal of Dundee university, is expected to examine options such as writing off the tuition loans of graduates who enter public-sector professions or paying golden hellos.
He is due to reveal the findings of his Gateways to the Professions report next year.