The Welsh education minister said the way kids were tested needed to develop their skills more.
Ten-year-olds will now be tested on number skills, how well they read and write, and problem solving.
Kids of 14 will be tested by their teachers, before they choose what GCSE exams they do.
Lots of teachers' unions and parent groups have welcomed the move, and one said the SATs "did not help teaching and learning".
But another teachers union, the NASUWT, said they thought scrapping the tests would mean more work for teachers.