Cumbria Police said 25 other people were treated for injuries, most of them children. Their injuries ranged from cuts to fractures and spinal injuries.
The coach driver, a 63-year-old man from Egremont who worked for J.B. Pickthall in Rowrah, west Cumbria, is in a stable condition in hospital.
Police said children from the same school who were travelling on a minibus behind the coach rushed to help their classmates.
Ch Supt Steve Johnson praised their actions, saying those who helped had "not thought about themselves".
"They went straight to the aid of their friends and colleagues and did an incredible job," he said.
Describing the teenagers who died, Mr Chapman said: "All I can say is they were Keswick School children and that makes them the most wonderful children in the world."
Tributes were also paid to Mr Short from Braithwaite, the car driver killed in the crash.
His wife Wendy described him as a "generous, principled man".
"He loved me and the family and was committed to his work with Barnardo's. As a parish councillor, Chair of Cumbria Rural Choirs and a former church warden, he was dedicated to the local community," she said.
Pupils praised for bus crash aid
Mr Chapman added that three teachers who were at the scene looked "very, very shaken" on Monday night but were back in work on Tuesday.
He said his feelings about the crash were "indescribable".
"We have a very large number of distressed children, we have a very large number of distressed staff, some of whom were down at the scene yesterday afternoon. We are all going to pull together today," he said.
"The children as ever were surrounded by their friends and people who wished to help and that is how it will be today."
He said the details of the crash were "very sketchy" and it was "a sight that very few students wish to see again in their lives".
Ch Supt Johnson added: "It's too early to talk about what caused this accident.
"As the incident commander, I can't help but be impressed that at a time of great need the emergency services and the community in West Cumbria once again have come together and done their utmost to try and help people and preserve life."
The bus was taking children home from Keswick School
The A66 was closed until 0300 BST on Tuesday to allow a thorough investigation of the crash scene.
Police urged people not to attempt to leave floral tributes at the crash scene.
Crosthwaite church in Keswick and nearby Braithwaite church had opened to receive flowers.
Moira Swann, director of children's services at Cumbria County Council, said her department would offer "all the help and support we can to the children, families and staff affected".
Educational psychologists were going into the school, which has about 1,000 pupils aged between 11 and 18, to offer support.
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