Currently, they can start school at the beginning of the term in which they have their fourth birthday.
But Powys council's cabinet approved the plans on Tuesday, which will see children start school in the September.
The change will be introduced from September 2017 and will save £1.2m a year.
The council also voted to increase the hours of free pre-school provision from 10 hours per week to 12.5 hours.
Councillor Arwel Jones, cabinet member for schools, said: "There's no secret that we are proposing this revised policy to help in our bid to meet the £27m budget savings target over the next three financial years."
He added: "Today's decision will bring us in line with the majority of other councils in England and Wales where children start school in the September after their fourth birthday."
Children in Powys will only be able to start primary school after turning four years old, it has been decided.