The children were rescued by members of the military, firefighters and civil aviation authority officials in the dense jungle of Colombia's Caqueta province, in the south of the country.
The 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 early on May 1.
"After arduous searching by our military, we have found alive the four children who went missing after a plane crash in Guaviare. A joy for the country," President Gustavo Petro said in a message via Twitter on Wednesday.
Three adults, including the pilot, died as a result of the crash and their bodies were found inside the plane.
The four children, aged 13, 9 and 4, as well as an 11-month-old baby, survived the impact.
Preliminary information from the civil aviation authority, which coordinated the rescue efforts, suggests the children escaped the plane and set off into the rainforest to find help.
Rescuers, supported by search dogs, had previously found discarded fruit the children ate to survive, as well as improvised shelters made with jungle vegetation.
Planes and helicopters from both Colombia's army and air force participated in the rescue operations.
