The Government's five-year plan, launched yesterday, will end the "Heath Robinson" system of funding, David Miliband, the schools standards minister, said.
Money for schools will be taken out of the Government grant that councils receive for all local services and ring-fenced for education.
Heads welcomed the change which will enable local education authorities to give them three-year budgets so that they can plan spending efficiently.
The Prime Minister promised three-year budgets earlier this year, but they would have been very difficult to introduce without a change in the funding system.
LEAs will continue to decide how the money is divided between individual schools and how much should be spent on primary, secondary and special needs.
Mr Miliband said: "This guarantees to schools that the budget voted by the taxpayer will go to local authorities and then to schools in a streamlined way."
But critics said the plans would make little difference. Ministers have been very successful in persuading councils to "passport" government money intended for education to schools. Only a handful have refused to comply.
Martin Rogers, co-ordinator of the local authorities' Education Network, said: "What's the difference between ring-fencing and passporting, anyway? The Department for Education and Skills has been better at policing passports than Blunkett and the Home Office."
There will be no national funding formula and the Government has no intention of funding schools directly from Whitehall.
A spokesman for the DfES said he expected that councils would continue to raise money for schools through council tax to supplement the Government grant.
Charles Clarke, the Education Secretary, told the education select committee that local authorities "continue to have a very important role to play. We are not taking LEAs out of education". He added that poor relationships between LEAs and the DfES contributed to last year's funding crisis. And he reaffirmed the Government's commitment to provide a guaranteed per pupil increase in funding for all schools in 20056.
David Hart, general secretary of the National Association of Head Teachers, said: "Three-year budgets with no money siphoned off to fund needless bureaucracy will be music to the ears of headteachers."
The five-year plan also promises 200 city academies to replace weak schools. Popular secondaries will be able to expand even if their neighbours have vacancies and ministers will make it easier for foundation status to be achieved.
Tony Blair said in a speech at London university's institute of education:
"It will be freedom for schools to succeed for all - not a free-for-all.
Our ambition will have at its heart a shift from good to excellent in the quality of education offered to the great majority of young people in this country.
"In terms of practical policy it is the most socially egalitarian vision any Labour government has ever espoused."