A-level and GCSE students in England will be given grades estimated by their teachers, rather than by an algorithm, after a government U-turn.
It follows uproar after about 40% of A-level results were downgraded by exams regulator Ofqual, which used a formula based on schools' prior grades.
GCSE results in England, Wales and Northern Ireland come out on Thursday.
Ofqual chair Roger Taylor and Education Secretary Gavin Williamson apologised for the "distress" caused.
Teachers' estimates will be awarded to students unless the computer algorithm gave a higher grade.
Mr Williamson said the results of mock exams - which critics said can be inconsistent across different schools - will now not be a key part of the appeals process.
In a statement, he acknowledged the "extraordinarily difficult" year for students, after exams were cancelled due to the coronavirus pandemic.
He said the Department for Education had worked with Ofqual to design "the fairest possible model" but it had become clear that the process of awarding grades had resulted in "more significant inconsistencies than can be resolved through an appeals process".
"I am sorry for the distress this has caused young people and their parents but hope this announcement will now provide the certainty and reassurance they deserve," said Mr Williamson.
He also revealed the temporary cap on the number of places that universities can offer to students would be lifted.
In a tweet, Labour leader Sir Keir Starmer said the government had been "forced into a screeching U-turn after days of confusion".
A-level students held protests across the UK in response to grades they said were unfairly awarded.
Ofqual chair Mr Taylor apologised for the "difficulty" caused to students over its grading system.
He told the BBC: "I would like to say sorry. We have recognised the difficulty that young people have faced coping with the receipt of grades that they were unable to understand the basis on which they had been awarded."
He added the regulator realised it had taken "the wrong road" and decided to "change course" after seeing the "anxiety" it had caused to young people and the added "administrative burden on teachers at a time when they need to be preparing for the new school term".
Alistair Jarvis, chief executive of Universities UK, said universities were being "as flexible as possible with applicants" but that the "late policy change" has created "challenges".
He called on the government to "step up and support universities", adding that Universities UK was seeking "urgent clarification" on a number of issues.
In a statement, the Universities and Colleges Admissions Service (Ucas) said about 69% of 18-year old applicants across the UK were currently placed with their first-choice university, which it said was "higher than at the same point last year".
It said students who did not have places at their first or insurance choice of university did not need to make their decision immediately.
Ucas said it would be issuing new advice for students and schools, which would be sent directly to students, as soon as they were able to take a decision.