The siblings were rescued by the military near the border between Colombia's Caqueta and Guaviare provinces, close to where the small plane had crashed.
The plane - a Cessna 206 - was carrying seven people on a route between Araracuara, in Amazonas province, and San Jose del Guaviare, a city in Guaviare province, when it issued a mayday alert due to engine failure in the early hours of May 1.
Three adults, including the pilot, died as a result of the crash and their bodies were found inside the plane.Â
The children, aged 13, nine, four and a now 12-month-old baby, survived the impact.
Narcizo Mucutuy, the grandfather of the three girls and one boy, told reporters he was delighted at news of their rescue.
"As the grandfather to my grandchildren who disappeared in the jungles of the Yari, at this moment I am very happy," he said.
Photos shared by Colombia's military showed a group of soldiers with the four children in the middle of the jungle.
"A joy for the whole country! The four children who were lost ... in the Colombian jungle appeared alive," Colombia's President Gustavo Petro said via Twitter.
Petro initially reported the children had been found on May 17 in a message on Twitter but later deleted the post, saying the information was unconfirmed.
"They were together, they are weak, let's let the doctors assess them," Petro told journalists on Friday, adding the children had defended themselves alone in the middle of the jungle.
"They found them - it makes me very happy."
Rescuers, supported by search dogs, had previously found discarded fruit the children ate to survive, as well as improvised shelters made with jungle vegetation.
Airplanes and helicopters from Colombia's army and air force participated in the rescue operations.
