Leeds Crown Court heard the school foundation, which was established in 1591, has never before been prosecuted.
The foundation's former fire risk assessor Doctor James Gibson, aged 65, of Earlswood Avenue, Roundhay, was also fined £10,000.
Prosecutor, Cassie Williamson said concerns were first raised after West Yorkshire Fire and Rescue Authority fire protection inspectors visited Wakefield Girls' High School's St John's building in February 2017.
That visit was to discuss building regulations for a proposed extension, but an inspector raised a number of concerns including coat hooks lining exit routes at the school.
In a follow up inspection, a number of other concerns were noted, including the removal of doors to cloakroom areas.
Inspectors also noted that devices fitted to several fire doors meant they would have failed to close in the event of a fire.
The court heard that during an inspection of Mulberry House Nursery School, which teaches children as young as three, on March 1, 2017, inspectors found that children’s coats and bags were being stored in an area that served a means of escape.
Miss Williamson said an inspection at Queen Elizabeth Grammar School revealed coats and bags were being stored in five areas classed as escape routes.
Wakefield Grammar School Foundation admitted to failing to make a suitable and sufficient risk assessment at Wakefield Girls’ High School and Queen Elizabeth Grammar School between February 16 and March 11 2017.
The foundation also pleaded guilty to failing to take general fire precautions at Wakefield Girls’ High School and Queen Elizabeth Grammar School between February 16 and March 11 2017.
Dr Gibson admitted failing to make a suitable and sufficient risk assessment at Wakefield Girls’ High School, Queen Elizabeth Grammar School and Mulberry House Nursery School between February 16, 2017 and March 11, 2017.
Saba Naqshbandi, mitigating for Wakefield Grammar School Foundation, said: "The foundation has impeccable good character with no previous convictions since being founded by Royal charter in 1591."
Ms Naqshbandi said the foundation relied on risk assessments provided by Dr GIbson, adding: "By its guilty plea it accepts those risk assessments were not sufficient."
Ms Naqshbandi said the foundation has carried out a review of fire safety policy and a new full time health and safety manager has been appointed.
Lee Hughes, mitigating for Dr Gibson, said he has had a successful health and safety career, adding: "He appears before this court with a great sense of embarrassment, shame and remorse."
Mr Hughes said: "He was mistaken as to the risks that these issues posed. He was absolutely rocked to the core to discover these risk assessments were wanting.
"There were no warnings or circumstances that indicated a risk."
Judge Robin Mairs fined Wakefield Grammar School Foundation £10,000 and handed Dr Gibson a £10,000 fine.
Judge Mairs said: " Wakefield Grammar School Foundation is centuries old. It has an impeccable record on safety hitherto."
Judge Mairs added: "There was full operation with the authorities and the regret they have expressed is genuine and heartfelt."
After the sentencing hearing Simon Chamberlain, chair of governors at Wakefield Grammar School Foundation, said: “The safety of all pupils, staff, parents and visitors is of paramount importance to Wakefield Grammar School Foundation and is kept under continuous review.
"The foundation wishes to emphasise that this case relates to historic matters, for which the foundation had, at the time, employed the services of an independent health and safety
"Despite this, we acknowledge our responsibilities as the owner of the buildings and as a "consequence accept the fine.
"Any breaches of fire safety regulations have been fully rectified to the satisfaction of the fire service and this has been confirmed in subsequent school inspections in 2017 and 2018.”