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."

Shaper/Caper will perform Within This Dust on 21 April as part of the museum's 15-year anniversary programme.
The show is inspired by the images of photographer Richard Drew, which capture a man falling from the World Trade Center during the attacks.
It was created by choreographer Thomas Small, who was previously BBC Radio 2's first Artist in Residence.
Mr Small, who was born and raised in Dundee, said the title of the show was inspired by an interview with a woman whose husband died in the attacks.
He said:  "She knew from watching the towers that her husband would be above the point of impact.
"Just as she answered her phone, the tower fell and she talked about how she fell to the ground at the same time as him and she grabbed the dust that was on the ground.
"She said that she felt that she was now within that dust."
Within This Dust was first performed in full at the Edinburgh Fringe in 2012 and has since been shown in Berlin and Sao Paolo.
Although it has been performed three times previously in New York, Mr Small said there was a "little" trepidation over its performance at the memorial museum itself.
He said: "The very first time we performed it in New York, we did it as part of a bigger festival and it really didn't sit in that programme of work.
"All the other bits were cabaret-style work and then there was this very, very sombre piece of work.
"No one clapped at the end at the end of the show and that was a real worry. I was really nervous about why that was.
"But then, very slowly there was a bit of a slow clap that eventually led to a standing ovation.
"Lots of people then came over and wanted to tell us their stories."
The dances in Within This Dust are accompanied by music and voices from witnesses to the attacks and relatives of those who died.
Mr Small said: "Wherever we've been in New York, people really want to take the time afterwards to sit down and thank us for making the work.
"People have obviously got quite extreme reactions to it.
"A lot of people get very upset. We've not had anybody angry, but lots of people were very emotional and crying.
"I think we have carried that into the work."
The invitation to perform at the 9/11 Memorial Museum came after its curator saw the show in New York last year.
Mr Small said: "She was really moved by it and was also crying and quite upset afterwards.
"They are adapting their auditorium and trying to accommodate ways in which the work might sit there.
"It marks the very first time a company has been invited to perform there, so we're pretty honoured, coming from Scotland."

Former Manchester City trainee Coulson, 22, joined Eastleigh from Oxford City in January 2016 and has scored six goals this season.
Muggleton, 21, moved to Barnet in 2014 and helped them win promotion back to the Football League two years ago.
Both players' moves are for undisclosed fees.
Find all the latest football transfers on our dedicated page or visit our Premier League tracker here.
Children in Powys will only be able to start primary school after turning four years old, it has been decided.
[NEXT_CONCEPT]
A Dundee-based dance company will be the first in the world to perform at the 9/11 Memorial Museum in New York.
[NEXT_CONCEPT]
Barnet have signed winger Luke Coulson from National League side Eastleigh, with left-back Sam Muggleton moving in the opposite direction.