The bodies of five-year-old Ruairi and Eoghan, aged 10, were found in a car crashed outside Westport in Co Mayo on Monday afternoon.
Earlier, gardaí had issued an appeal to help find the boys and their 43-year-old father Sanjeev Chada.
It is the first time a Child Rescue Ireland alert, designed to help locate abducted children when there is serious concern for their safety, has been issued since the system was put in place last year.
It is understood detectives do not believe the children died from injuries sustained in the crash.
There’s great sorrow in Co Carlow – the boys’ mother is distraught.
Sam Smyth, journalist
The boys and their father were last seen at the family home in Ballinkill, Co Carlow, at 6.30pm on Sunday when they left to go bowling at the Dome Bowling Centre in Carlow town.
They failed to return home that night and were reported missing at 1.30am.
Tributes have been paid to the little boys, hailing them both as hugely popular sport fanatics.
Local parish priest Fr Declan Foley told RTÉ that he was in the family home when the news was broken to their mother Kathleen, who is a nurse from the Carlow area.
"You can't put into words the shock and numbness and pain and grief of that news coming through," he said.
"They're her two boys - her pride and joy. The community itself is absolutely ruptured by this sad news."
It is understood Mr Chada has also been injured and taken to hospital following the single-vehicle crash on the Westport to Louisburgh road. His condition is not thought to be serious.
Gardaí have confirmed that the crash scene is being preserved for forensic examinations.
A spokesman said: "Gardaí are appealing for anyone who may have witnessed this traffic collision, or anyone who may have observed a dark green Ford Focus 06 CW 238 between 6.30pm on Sunday evening and 4pm on Monday afternoon, to contact the incident room at Westport Garda Station."