Seven year olds in England will not all have to sit national tests at the same time next spring, ministers have announced.
The progress of pupils will be monitored by their teachers
Instead there will be a more flexible approach, focusing on teachers' judgements of how pupils are doing.
The decision to change the testing regime follows a successful pilot scheme in 5,000 schools.
This showed teacher assessment, with a more flexible test, was more accurate than raw test results.
Children will still sit the Key Stage 1 national curriculum tests - often known as Sats - in English and maths, but not at a fixed time.
And there will be much more emphasis on work done throughout the year.
The final mark given to pupils will be their class teacher's assessment of how they have done, rather than a test score.
The pilot this year was carried out in almost a quarter of education authorities.
The evaluation of it, by researchers at Leeds University, found that the new arrangements were "at least as robust" as the system in which tasks and tests and teacher assessment are reported separately.
They found most teachers reacted positively, recognising opportunities to reduce workload and enhance their professionalism.
The confidence of some teachers in making assessments was low at
the beginning of the trial, but grew as they came to understand and implement the new arrangements.
There was what the researchers called "a notable feature" in the reaction of parents.
They tended to be much more confident in the judgements of their own child's teacher, whom they knew and trusted, than teachers in other schools, "whose motives were mistrusted, and whose professionalism was not recognised".
But the report said there was "no evidence" that teachers had used the new arrangements to inflate their school's results.
Education Minister Stephen Twigg said: "For seven year olds, a teacher's overall, rounded assessment of a child's progress through the year, underpinned by national tests, will provide a more accurate guide to their progress than their performance in one set of tasks and tests."
This new emphasis on trusting teachers to judge pupils is welcomed by the unions.
National Union of Teachers head of education John Bangs said the change meant teachers' assessments could override test results.
"This is a fundamental shift in the testing regime in place since 1993," he told BBC Radio 4's Today programme.
But teachers would have preferred the tests to be scrapped altogether, he added.
Liberal Democrat education spokesman Phil Willis felt the same.
"Assessment must be built around the benefit of children and not around the fulfilment of government targets," he said.
David Hart, general secretary of the National Association of Head Teachers, also welcomed the plans, saying they would improve teacher morale.
"It demonstrates that the government, at long last, recognises that teachers can be trusted and that teacher assessment is the right way forward for seven year olds," he said.
"I doubt very much whether the vast majority of seven year olds will know they are being tested, so we'll get rid of the problem of stress."
There have also been calls for the approach to be extended, at least to the external tests taken at the end of primary school.
The Association of Teachers and Lecturers (ATL) said it had consistently voiced its concerns, particularly about "the demotivating effects of Sats on pupils who are struggling to achieve" and the extent to which testing, not learning, dictated the education agenda.
Its deputy general secretary, Gwen Evans, said: "Given the success of the Key Stage 1 trials, the time is now right to take a closer look at Key Stage 2."
The Secondary Heads Association said the government should also put greater reliance on the professional judgement of teachers at Key Stage 3.
It said this year¿s "marking fiasco" had further shaken confidence in the English tests in particular.
But Mr Twigg said there were no plans to do either.
"It is important for schools and parents to have information on a child's performance through objective, nationally benchmarked tests for ages 11 and 14," he said.