CfBT Education Trust, the owner of the school, had said the running of Kings Monkton was unsustainable because of annual financial losses of more than £250,000. It had been at risk of closure at the end of the summer term if an alternative provider was not found.
McCarthy is the founder of Orbis Education & Care and led the company through a merger with Ludlow Street Healthcare Group. He remains a director and shareholder of Ludlow Orbis Group.
Kings Monkton School is the first mainstream school acquisition for Heathfield Independent Schools, but the company's long-term aspiration is to grow its portfolio of mainstream schools in Wales organically.
Jonathan Greenwood, chairman of Kings Monkton Trustees, said: "Our aim has always been to try to secure a sustainable future for Kings Monkton School. While we knew CfBT could not continue to run the school it was never our intention to let down staff, students and parents by closing the school but to find a new provider who could help the school to flourish.
"I am delighted that Heathfield Independent Schools and Andrew McCarthy intend to take over the school and are committed to providing first-class, value-for-money independent education."
McCarthy added: "My team and I are really pleased to be taking over Kings Monkton School and securing its future. It is a prestigious school with a celebrated history and now a bright future.
"We do plan to make some changes to the school. We want to improve the environment and facilities here, we want to develop a programme of extracurricular activities and we need to invest heavily in marketing the school to attract new pupils.
"While the deal was agreed at the beginning of the week, there will be a period of due diligence that we will now enter into which will take place over the next three weeks, before the agreement becomes concrete. We hope that we will be in a position to move forward by the end of the month and start the building blocks to ensure the future success of the school."