Nick Clegg has drawn dividing lines with the Tories over education by insisting all schools should have qualified teachers and follow a core curriculum.
The Deputy Prime Minister unveiled the manifesto commitment for next year's general election with the row over "Trojan Horse" extremist schools still raging.
A senior Lib Dem source said the controversy in Birmingham showed how easy it had become for headteachers and governors at academies and free schools to drop subjects they did not approve of.
"Liberal Democrats want more teachers and schools to enjoy freedom from Whitehall diktats," Mr Clegg said.
"But that does not mean parents and children should not have some basic safeguards.
"There is no reason why a child attending an academy or free school should not enjoy the same basic right to be taught by a qualified teacher or to follow a core curriculum as any other child.
"These changes will guarantee parents that, whichever school their child attends; they will enjoy a world-class education that will help them fulfil their potential."
Schools Minister David Laws added: "We know that these reforms enjoy the support of teachers and parents and respond to the recommendations of Ofsted made this week."
Academies and free schools are subject to rules, such as being not-for-profit, complying with Ofsted inspections and employing a qualified special needs coordinator.
However, unlike state-maintained schools, staff do not require Qualified Teacher Status (QTS), and they have broad control over curriculum.
The Lib Dem source stressed that it had been Tory Education Secretary Michael Gove's decision to exempt them from QTS rules, while the curriculum policy had been set under the previous Labour government.
Mr Clegg's announcement brings his party into closer alignment with the Opposition, which says staff at academies and free schools should have qualified status.
In the wake of the Ofsted investigation in Birmingham, which saw five institutions put into special measures, Mr Gove said in future all schools would be required to promote "British values".
David Cameron said those values would include "freedom, tolerance, respect for the rule of law, belief in personal and social responsibility and respect for British institutions".
A Conservative Party source said: "The Liberal Democrats helped us massively extend academy freedoms by voting for the Academies Act in 2010.
"It's thanks to the votes of Liberal Democrat MPs that 4,000 schools now have the freedom to set their own curriculum, compared to just 203 schools four years ago.
"It's obviously a shame if the Liberal Democrats now want to roll back those freedoms.
"We are taking power away from politicians and bureaucrats in Whitehall and handing it to heads and teachers, as they are the ones who know their pupils best."
Chris Keates, general secretary of the NASUWT teachers' union, said Mr Clegg was "delusional" for thinking the announcement will overshadow the role the Lib Dems have played in "betraying" schoolchildren by supporting the Tories in removing the previous requirement for qualified teachers in schools.
He said: "Children and young people are entitled to be taught by a qualified teacher and to follow a broad and balanced national curriculum.
"Until this coalition took office, that's what they had.
"Without the support of the Liberal Democrats, the Conservatives could not have removed the requirement for schools to employ qualified teachers.
"Without their support, schools could not have been given freedom to choose their own curriculum.
"Nick Clegg and the Liberal Democrats are delusional if they think this announcement can airbrush out the key role they have played in betraying our children and young people by colluding with the Conservatives in the introduction of education policies which have robbed our children and young people of these important entitlements.
"Teachers, parents and the public would be right to question why Nick Clegg, the Deputy Prime Minister, is not insisting these provisions are restored now rather than making them a manifesto commitment."