At night, they built campfires both for warmth and to signal possible rescuers. They were eventually spotted by a helicopter crew and a paramedic was lowered. He found them safe but weak.
Both lost weight, but were in good health and are now on special diets.
The friends informed their families that they'd intended to set out from Fukkon in Chile on what should have been a three-day trek, starting Oct. 13, on a trail through a national park.
Their parents became worried when they did not hear from them. Tomer's parents, Motti and Rahel, initiated a search operation and then flew out to Fukkon the following day. News of the disappearance was broadcast locally.
"I really do believe that Motti and Heli [Rahel] saved my son's life as well as Tomer's," said Itamar's mother, Josanne Ben-Hur.
"The marvelous thing is how the boys survived for 21 days without food. They wrote diaries, took photographs of one another. Itamar had a Tom Clancy book, which they read to each other in English. They supported one another. When Itamar was down, Tomer supported him and vice versa.
"The thought that kept them going was the fact that they knew that their families would come and look for them. Tomer kept saying that his father would come and find them, and they did. They found them," said Josanne Ben-Hur.
The two searched for food in their immediate surroundings but to no avail, and could not even see any animals to hunt. The ants were their only source of nourishment.
The Israeli Embassy in Chile was "incredibly helpful, " said Josanne Ben-Hur, and the staff there did "everything possible" to assist.
"The ambassador telephoned me personally to say that the boys had been found and were safe and physically fine," she said.
The two are now recuperating at a holiday home in Fukkon before deciding whether to continue with their trip once they have fully recovered.
"We are not going to tell them to come home," said Josanne Ben-Hur. "It has been a traumatic experience for them but it's like falling off a horse and getting back on again. If they came back straight away they would probably regret it."