The main concessions included a guarantee that councils will continue to have a "strategic" role over school admissions, the Government's code on admissions policy will be given legal force, and parental interviews for selection banned.
The U-turn was spelled out in a letter by Ms Kelly to MPs last night, which was obtained by The Independent. She said the Bill would translate into law fair admissions promised in the White Paper "so that no trust school or any other maintained school can undertake any further selection by academic ability".
On the code of practice, Ms Kelly said the requirement on schools to "have regard" to the code would be toughened to force them to "act in accordance" with it.
She rejected a proposal by the Commons Select Committee on Education for local authorities to be given a new role by setting quotas on fair access to schools for pupils from poorer backgrounds.
The Education Secretary said the admissions forums would be given "power to produce an annual report setting out the detail of local admission arrangements, how they impact on fair access and how particular groups are faring".
She added: "It would be wrong for the forum to seek to set quotas for different types of children in each school, but this report may of course include details of FSM [free school meals] and other characteristics of the intake in each school."
Local authorities will not be given a role to stop popular schools expanding, but she said a school adjudicator would have to take account of fair access and the local authorities' strategic plans in settling disputes. When setting up schools, local councils will be able to set out the communities they should serve.
On trust status, she bowed to demands that the community should have a majority among the governors of trust schools, rather than private sponsors, saying: "Where the school wants it, a trust will be able to appoint the majority of the governors. Of course there will be many cases where the trust and the school will not want a majority, but we believe that this is an issue best left to schools and parents to decide and not for Whitehall to impose."
To avert fears of asset stripping, the assets of trust schools will revert back to the governing body where trust status is removed.
The schools commissioner, she added, "will not decide school organisation matters - that will be for local authorities (with appeals to the schools adjudicator). Of course, decisions about the acquisition of trusts will be taken by schools themselves."
The package split the Labour critics and appeared to have done enough to avoid the humiliation of Mr Blair relying on David Cameron and the Tories to get the Education Bill through the Commons. The Tories may seek to oppose parts of the Bill for retreating too far. Some of the rebels, including the former local government minister Nick Raynsford - who led opposition to the education White Paper - signalled they were ready to accept the compromise package.
Mr Raynsford said: "I am hopeful that there will now be a basis on admissions policy, the role of local authorities, arrangements for the expansion of schools to ensure all schools within an area are able to achieve their maximum, these new arrangements do hold out the prospect of agreement."
He said he hoped the calls for Ms Kelly to resign would subside. Mr Blair has a reshuffle in the offing, but it is likely that Ms Kelly has done enough to avoid the humiliation of being dropped or moved, and will be given the task of steering the Bill through the Commons in March.
Quotes from Ruth Kelly's letter
* "We entirely understand why ... people want clear assurance the purpose of reforms is neither a backdoor way of reintroducing academic selection nor preventing local authorities carrying out necessary strategic priorities."
* "We will ensure ... no trust school or any maintained school can undertake any further selection by academic ability ... We will close the legal loophole so admission authorities must 'act in accordance' with it, rather than having to have 'regard' to it."
* "In fulfilling its leadership role in relation to school organisation ... a local authority may choose to set out its strategic plans, and report on its progress ..."Reuse content