The head of private school Epsom College and her husband and seven-year-old daughter were discovered dead on a property on school grounds.
Emma Pattison, 45, her husband George, 39, and their daughter Lettie were discovered dead on Sunday at 01:10 GMT.
Police said they were confident it was an isolated incident “with no third-party involvement”.
They were summoned to the school in Surrey by the local ambulance service.
An investigation is underway to determine the circumstances surrounding the deaths.
Detective Chief Inspector Kimball Edey said: “On behalf of Surrey Police, my team, and I, I first want to express my sincerest condolences to the friends and family of Emma, Lettie and George, as well as to the students and staff of Epsom College, for their tragic loss.
“I want to give my assurance that we will conduct a thorough investigation into what took place… and hope to be able to bring some peace in these traumatic circumstances. I would ask that their privacy is respected at this very difficult time.”
Ms Pattison became Epsom’s first female head only five months ago, in September 2022, after six years as headteacher of Croydon High School in south London.
According to Companies House, the head teacher’s husband, George, was a chartered accountant and the director of a management consultancy firm called Tanglewood 2016.
The chair of the board of governors at the school called his late colleague “a wonderful teacher, but most of all, a delightful person”.
“On behalf of everyone at Epsom College, I want to convey our utter shock and disbelief at this tragic news,” Dr Alastair Wells said.
“Our immediate thoughts and condolences are with Emma’s family, friends and loved ones, and to the many pupils and colleagues whose lives she enriched throughout her distinguished career.
In October, Ms Pattison tweeted she was “thrilled” that Epsom College had won the Independent School of the Year 2022 award.
Ms Pattison’s daughter attends Croydon High School, where Sheena previously worked.
The parent, who only wished to give her first name, said the news was “an utter shock and tragedy”.
“During her time as head teacher, she turned the school around, and she did so many things that enriched the children’s lives,” she told BBC News.
“She was slight but very formidable, she knew all of the pupils by name. She was everything you could want in a principal.”
Epsom College requested “time and space” to process “these shocking events” in a statement issued late Sunday night.
“We ask that the public and the media respect the privacy of Emma’s family, and help us to prioritise the needs of our pupils,” the school said.
“The news is heart-breaking and we need time and space to come together and process these shocking events. No further statement will be issued at this time.”
The school has appointed Paul Williams as acting headmaster.
Local MP Chris Grayling has also expressed his shock at the incident.
“This is an appalling tragedy and my heart goes out to their family and friends and to everyone at Epsom College as well as at the little girl’s school,” he said.
Inspector Jon Vale, Epsom and Ewell’s borough commander, said: “We’re aware that this tragic incident will have caused concern and upset in the local community.
“While this is believed to be an isolated incident, in the coming days our local officers will remain in the area to offer reassurance to students, parents, teachers and the local community.
“I would like to thank the school and the community for their understanding and patience while the investigation continues.”
The three deaths, according to Surrey Police, have been reported to the coroner.
The College charges more than £42,000 per year for boarding students, and its alumni include Conservative MP Sir Michael Fallon, broadcaster Jeremy Vine, and his brother, comedian Tim Vine.
The school, which accepts both boys and girls, was founded in 1853 and prides itself on consistently ranking among the top schools in the United Kingdom based on exam results.