The pupils were the first to try the new National Curriculum, which "raised the bar in terms of expectations of young people’s mastery of literacy and numeracy".
They are also the first to be marked with the new primary school testing system of 'scaled scores'.
More than half (53%) of pupils met the new expected standing in reading, writing and mathematics.
"This is the first year we have assessed pupils under the new more rigorous system and it is no surprise that this year’s results look different to previous years, but despite that the majority of pupils have achieved above and beyond the new expected standard," said Education Secretary Nicky Morgan.
"Nothing is more important than ensuring that young people master the basics of reading, writing and mathematics early on."
"As part of this government’s commitment to delivering real social justice, we have raised the bar on what counts as a good enough standard in the 3Rs for our children by the end of primary school," Morgan added.
However, Russell Hobby, general secretary of school leaders’ union NAHT, disagreed that the results showed children have achieved "above and beyond".
"We have learned today that only 53% of children have met the new expected standard in reading, writing and maths," he said.
“The government has decided that nearly half of pupils have failed at the end of their primary education.
"This is not representative of the quality of their education, nor of the hard work pupils have put in this year."
53% of pupils met the new expected standard in reading, writing and mathematics.
66% of pupils met the new expected standard in reading.
70% of pupils met the new expected standard in mathematics.
72% of pupils met the new expected standard in grammar, punctuation and spelling.
74% of pupils met the new expected standard in writing.
The results are not comparable to test results from previous years, which were under an entirely different system of assessment.
Morgan said it is important that parents and children see these results for what they are - "a reflection of how well children this year have performed against a new curriculum" - rather than make comparisons to last year.
But Hobby said it's "impossible" for parents and teachers not to compare.
"Parents and teachers already know that assessment this year has been chaotic and confusing," he said.
"It will be impossible for parents not to compare this year’s percentage with last year and not to worry that the new, higher expectations mean that their children appear to have performed worse than children in previous years.
“The simplest way to guarantee that this doesn’t happen is to not publish the data for 2016 in league tables.
"However, the government still insists on making the results public, even though it is clear that it’s not useful for parents to judge either how good a school is or how well their child is performing."
For the Key Stage 2 results, test results were converted into ‘scaled scores’ - with a score of 100 being the expected standard.
Any score below this means the pupil is working ‘towards the expected standard’, and any score above means the pupil is working ‘above the expected standard’. Previously the expected standard was a level four.
This year the average scaled score in reading is 103, the average scaled score in mathematics is 103 and the average scaled score in grammar, punctuation and spelling is 104.
The DofE has also released a Q&A guide for parents addressing queries they may have.