The tests will be a week later than scheduled after Education Secretary David Blunkett became concerned that next year's late Easter holiday could depress results.
He feared that children would underperform if they sit the English, maths and science tests almost immediately after Easter.
Heads complained about the original dates after they discovered that some schools were to start the summer term four days before the primary tests.
The key stage 2 tests are normally taken during the second week of May by 600,000 11-year-olds. Similar tests for secondary pupils are taken by 14-year-olds during the preceding week.
The results of the KS2 tests are particularly important for ministers as they are the basis for ambitious government literacy and numeracy targets. Mr Blunkett has promised to resign if 80 per cent of 11-year-olds fail to reach the required standard in English and 75 per cent in maths by 2002.
David Hart, general secretary of the National Association of Head Teachers, said: "We alerted ministers to the concerns of many of our members who were particularly concerned that children with English as a second language and those with special needs would be unfairly disadvantaged by the early test dates.
"This is another recognition of the way in which the Government is responding positively to genuine concerns."
This year the KS2 tests began on May 10, five weeks after Easter, giving schools several weeks to prepare pupils for the tests.
Next year, however, Easter falls nearly three weeks later, on April 23, and the tests were provisionally scheduled to start just two weeks later, on May 8. They will now begin on May 15 and key stage 3 tests will take place in the week beginning on May 8.
Children's performance is well known to slump immediately after a school holiday as they "unlearn" what they learned the previous term.
Schools were due to receive written confirmation of the new dates today from the Government's curriculum quango, the Qualifications and Curriculum Authority, which is responsible for the tests.