Teachers will be asked predict what grades their students may have achieved if exams had gone ahead, following their cancellation owing to coronavirus.
GCSEs, A-Levels and SATs have been cancelled as schools across the country will begin to close from Friday to stop the spread of Covid-19.
Exam boards will ask teachers to take into account "a range of evidence and data", such as mock exam results and other school work.
The calculated grades will be "a best assessment" of the work students have put in, the Government said.
The results are expected to be formalised in July. Typically, A-level and GCSE grades are usually published mid-August.
Students will also have the option to sit an exam in the next academic year, scheduled to start in September, or in summer 2021, the Department for Education said.
Pupils will also be able to appeal against their grades if they do not think they are correct.
Education Secretary Gavin Williamson said: "Cancelling exams is something no Education Secretary would ever want to do, however these are extraordinary times and this measure is a vital but unprecedented step in the country's efforts to stop the spread of coronavirus.
"My priority now is to ensure no young person faces a barrier when it comes to moving onto the next stage of their lives - whether that's further or higher education, an apprenticeship or a job.
"I have asked exam boards to work closely with the teachers who know their pupils best to ensure their hard work and dedication is rewarded and fairly recognised."
Geoff Barton, general secretary of the Association of School and College Leaders, said the teacher assessment system outlined by the Government "leaves many questions unanswered and will clearly require more detail".
But he added the union is "confident that Ofqual, the exam boards, schools, and colleges will do everything possible to ensure grades are awarded fairly and consistently in these difficult circumstances."
Mr Barton added: "Teachers are experts in their subjects, they know these qualifications inside out, they know their students, and they have the professional skills to assess them accurately.
"We do not subscribe to the notion that exams are the only credible way of assessing qualifications, and this is an opportunity to at least point the way to a less brutal system."
As well as academic qualifications, many students will have been due to take exams for vocational courses this summer.
The Government said that these vocational qualifications are offered by a wide range of awarding bodies, with different types of assessment.
In many cases, it said, students will have completed modules or work that could be used to help calculate a grade.
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