Teenagers in England who fail to achieve at least a grade C in English and maths GCSEs will have to continue studying the subjects from this term.
It means hundreds of thousands of youngsters in school and college will have to carry on with the subjects until the age of 18.
Employers have warned that young people need to improve these skills.
Education Secretary Michael Gove said the subjects were the ones "employers demand before all others".
Head teachers said they supported the principle of the change but there was "genuine confusion" about how it would be implemented.
The Association of Colleges says it will require 1,100 extra maths teachers and 1,000 more English teachers.
Up until now, pupils have been able to drop the subjects at the age of 16 without having gained a qualification in them.
Many would never study these subjects again, prompting concerns from employers' organisations that too many young people lack literacy and numeracy skills necessary for work.
Last year, there were more than a quarter of a million 19-year-olds without a C grade in English and maths.
Teenagers who missed C grades will either re-take GCSEs in maths and English, or else there will be an option to take other types of maths and English lessons. But they will be required to continue studying the subjects.
In a separate measure also being introduced, the participation age for education and training is being increased to the age of 17. It will mean young people will be expected to remain in some kind of education or workplace training, although there will be no sanctions as it is phased in.
Skills minister Matthew Hancock said the requirement to keep studying English and maths was not about re-sitting exams but about continuing to develop these essential skills.
"For those who fail to get a C at GCSE, it's a huge impairment to their future life, their ability to participate not just in work but also as a citizen," he said.
Mr Hancock said that most of those who did not attain a grade C at the age of 16 continued to a further education college and the there was a programme to increase the number of English and maths teachers at those institutions.
Joy Mercer, director of policy at the Association of Colleges, said further education colleges would need an extra 2,100 experienced teachers.
"Young people, who have often tried to succeed at maths and English more than once, need the most experienced teachers to motivate them, not those who have just left a university course," she said.
Brian Lightman, leader of the Association of School and College Leaders, said the "aim is right, but there are many questions the government needs to address urgently about how it will fund and implement its plan".
The head teachers' leader said there needed to be clarification about funding for extra classes and teachers.
"There is still genuine confusion about the announcement today and what the new policy means, on the day that schools and colleges are supposed to start implementing it," said Mr Lightman.
The importance of developing English and maths beyond the age of 16 had been put forward by Prof Alison Wolf in her report on improving vocational education for 14 to 19-year-olds.
She found that too many vocational qualifications lacked value for employers and too many youngsters were entering adult life without adequate skills in literacy and numeracy.
"Good English and maths grades are fundamental to young people's employment and education prospects," she said.
"Individuals with very low literacy and numeracy are severely disadvantaged in the labour market."
Prof Wolf, professor of public sector management at King's College London, welcomed the implementation of her proposals.
“Every other country in the developed world concentrates on improving the language and maths skills of its post-16 students, and so should England. Recognising the central place of English and maths skills in society is long overdue," she said.
These changes apply to young people in England. The Welsh government says that it already has plans that will require learners to continue English and maths beyond the age of 16 from 2015.
"Learners who do not achieve these GCSEs at A*-C in Key Stage 4 will be required to continue to pursue them in post-16 learning. Learners who do achieve these GCSEs in Key Stage 4 will continue to develop their skills by following Essential Skills qualifications," said a spokeswoman for the Welsh government.
But Labour’s shadow education secretary, Stephen Twigg, said more urgent action was needed.
"In 2012 Labour set out ambitious plans for all children to study English and maths to 18.
“A whole wasted year later and the government have only got half way there. This isn't good enough. David Cameron needs to listen to employers - they want all young people to continue building these key skills to 18."
The Institute of Directors said that so many young people not achieving good qualifications in English and maths was "socially damaging and economically unsustainable".
The CBI backed the changes but also called for "high-quality vocational routes as well as academic ones".
Christine Blower, general secretary of the National Union of Teachers, said: "It's critical the government works with schools and colleges to make sure that what is on offer for those young people is not marching them in and out of the exam room, but actually making sure they are developing by having an appropriate curriculum."