The bodies of the pilot, the children's mother and a relative were all found at the crash site, where the plane sat almost vertical in the trees.
A massive search by 160 soldiers and 70 Indigenous people with intimate knowledge of the jungle had been under way ever since for the youngsters, garnering global attention.
The area is home to jaguars, snakes and other predators, as well as armed drug smuggling groups, but ongoing clues -- footprints, a diaper, half-eaten fruit -- led authorities to believe they were on the right track.
Worried that the children would continue wandering and become ever more difficult to locate, the air force dumped 10,000 flyers into the forest with instructions in Spanish and the children's own Indigenous language, telling them to stay put.
The leaflets also included survival tips, and the military dropped food parcels and bottled water.
Rescuers had also been broadcasting a message recorded by the children's grandmother, urging them not to move.
Huitoto children learn hunting, fishing and gathering and the kids' grandfather, Fidencio Valencia, had told AFP the children are well acquainted with the jungle.
"Today we have had a magical day," Petro told the media upon his return from Cuba, where he signed a six-month truce with Colombia's last active guerrilla group, the ELN.
"Getting closer and attaining peace in the agreement that is moving forward with the ELN... And now I return and the first news is that indeed the Indigenous communities that were in the search and the military forces found the children 40 days later," he said.
"They were alone, they made it on their own. An example of absolute survival that will go down in history," he said.
Seventeen days after the children went missing, Petro announced that they had been found alive, but he retracted the statement a day later, saying he had been given false information.
On Friday, he praised "the effective coordination between the military and the Indigenous people" during the search, saying it was an "example of an alliance for the country to follow."
Valencia told AFP that the children had been found by a native of Araracuara who had been participating in the search.
"I need a flight or a helicopter to go and get them urgently," the grandfather said.
Defense Minister Ivan Velasquez paid tribute to the various army units' "unshakeable and tireless" work, as well as to the Indigenous people who took part in the search.
Army rescuers "immediately took charge of and stabilized" the four siblings, who were to be transferred to San Jose del Guaviare, according to the minister.
"Tomorrow, depending on their medical assessment and condition, we hope they will be transferred to Bogota, to the military hospital," Velasquez had said.
It was later said that the children reached Bogota.
