Whitton Primary School, near Knighton, opened in a village barn in 1724, before re-opening as a school house in 1767.
The closure is due to low numbers, and the cost per pupil being "significantly above the county average" Powys council said.
Residents objected to the closure of the 15-pupil school.
The council's cabinet approved the closure in July 2014, but following objections it was referred to Education Minister Huw Lewis, who upheld the decision.
Wealthy benefactor Dame Anna Child left her Â£500 fortune to build a school in the "village she loved" after she died in 1703.
"She wanted to provide a salary for someone to teach the children in the parish," said Graham Skipworth, chairman of governors for the school.
The school is funded by the local authority but is backed up by the Dame Anna Child's Endowed School Trust.
The trust raised money from the 147 acres (59 hectares) of farmland surrounding the school which it purchased three centuries ago.
Funds raised have been used to support staffing to improve teacher to child ratios, as well as purchasing extra computer suites for the classrooms.
Now it will now be used to provide parents of the children leaving with uniforms for their new schools.
A Powys village school funded by an aristocrat for 291 years will close on Friday.