Eleven-year-old Addison Stewart, and Zane Mellor, Jye Sheehan, Jalailah Jayne-Maree Jones, Peter Dodt, all 12, were on Friday formally identified with permission from their families.
Three other children remain in a critical condition, a day after a gust of wind sent the jumping castle 10 metres into the air during year-end celebrations at Hillcrest Primary School.
One child who was taken to hospital has been discharged and is recovering at home.
Investigations by police and WorkSafe Tasmania officials at the Devonport school are ongoing and will examine whether the castle was tethered.
"That forms part of the investigation ... we all have a lot of questions," Tasmania Police Commissioner Darren Hine said.
"This means you'll have some questions that we're not able to answer, as many details will be a matter for the coroner."
About 40 students in Year 5 and 6 were taking part in activities on the last day before summer holidays, Mr Hine said.
The gust also picked up several inflatable zorb balls, with Mr Hine indicating the majority of the children were inside the jumping castle.
Some of the messages outside the school read "rest in peace beautiful angels" and "God is watching over you".
Local father and counsellor Brad, who lives in the neighbouring suburb, has been stationed outside the school handing out water bottles to visitors.
He said hundreds, if not several thousand people, had stopped to pay their respects.
"The biggest thing will be the ongoing trauma, when the flowers are gone and things go back to normal," he told AAP.
A woman, who left a gift but didn't wish to be named, said the community was very much still in shock.
"Overnight there has been an enormous outpouring of grief," said Tasmanian Premier Peter Gutwein, who was among those to leave flowers.
"As a parent, I cannot understand how the parents of those who have lost children must be feeling.
"It is devastating, heartbreaking. It's just simply incomprehensible."
Fiona Morrison, a member of the local Uniting Church, said some people had turned off their Christmas lights as a mark of respect.
Australian Education Union representative David Genford said teachers from across the world had reached out to their Tasmanian counterparts.
"This touches everyone. I know as a teacher myself, there are times when you're supervising this type of activity," he said.
"This shouldn't happen. It's such a tragedy."
Three online fundraising pages have been set up to support the affected families, with one created by Devonport local Zoe Smith raising more than $730,000 by Friday afternoon.
Hillcrest Primary School was holding a 'Big Day In' celebration to mark the end of the school year.
Several adults who were there during the incident provided first aid before emergency authorities arrived.
Devonport Mayor Annette Rockliff said people were trying to get their heads around what happened.
"Everybody knows somebody and we are already seeing people wrapping their arms around each other and supporting each other. I know that that will continue."
Tasmanian Governor Barbara Baker and Prime Scott Morrison have extended their sympathies to the families and the community.
