Tuakau College principal Chris Betty said Toni came from a well-known family within the school.
Three of Toni's siblings are also students at the college.
"He was a bit of a character - a likeable character - and he worked really hard," Mr Betty said.
"It's really sad for us, as a school community, and the whanau is getting strong support."
Mr Betty said representatives of the college visited Toni's family this morning.
The school was also working with the Ministry of Education on counselling services for students affected by the death.
An assembly would be held tomorrow to inform students of Toni's death and also offer them support.
Dozens of tributes have appeared on social media, with many young people calling for the swimming spot to be closed off to the public.
"Rip to another brother Toni. Shucks, man. Gone [too] fast. I know the heavenly father will look after you," one friend wrote.
"To your family, stay strong and know that the plan of salvation is true. He's always with you. Sorry for your loss and much love. They should close Hunua Falls."
Toni was with family members when he got into difficulty while swimming at the popular spot. A family member attempted to rescue the youngster, but was unsuccessful.
Another teenager - an older relative - dived in but "had to let go" after the younger boy got into trouble while swimming at Hunua Falls, southeast of Auckland, yesterday about 3pm.
A police spokeswoman this morning confirmed the body of the missing 13-year-old who disappeared swimming at the popular south Auckland waterhole was found last night.
Police said members of the National Dive Squad recovered his body night just after 10:30pm.
The teenager was at the swimming hole with members of his extended family when he got into difficulties in the water yesterday afternoon.
A member of his family tried to rescue him however the effort was unsuccessful.
His family were now being supported by Police and Victim Support.
At least 17 people are believed to have died at the falls before the latest tragedy, and there are now calls for urgent action by the Auckland Council to prevent further drownings.
Grieving relatives of 17-year-old Peter Lemalu, who drowned at the falls just nine days earlier, believe the area should have been shut down years ago.
Yesterday, distraught relatives and members of the public attempted to find the boy after he slipped under the water, said Senior Sergeant John Yearbury, of Counties Manukau Police.