Children's Secretary Ed Balls heralded the end of the current system of national Sats tests for 11-year-olds as he announced a major review of primary education.
Mr Balls said he wanted a more "flexible" assessment regime, allowing pupils to take tests when they are ready instead of at a fixed age.
He acknowledged it was "time for a change" in the way children are tested and ordered a full-scale overhaul of the primary school curriculum.
The minister's remarks follow years of campaigning by teachers' unions and a flurry of reports warning that the pressure to perform in tests is damaging children's education.
Last week, headteachers warned that schools felt under so much pressure that some teachers had even resorted to cheating in order to boost Sats results.
Mr Balls said the proposals for a new testing regime would be contained in the Government's 10-year Children's Plan, to be published on Tuesday.
He told the BBC's Andrew Marr Show that he would not be abolishing national tests completely because parents "want to know not only about their child but how their school is doing".
"Our Children's Plan will pave the way for a change away from the rigidity of the national testing we have at the moment - which says that every child does the same test at the same age - towards testing which is more in line with the needs of the child," he said.
Mr Balls said the entire primary school curriculum would be overhauled as part of the Children's Plan.
Former Ofsted director Sir Jim Rose, who led a Government inquiry into the teaching of reading, will head the "root and branch" review, which will establish the essential knowledge and skills that schools will teach five to 11-year-olds for years to come.
