Another woman on their boat died from dehydration and her body was thrown overboard, with two of those picked up seriously ill.
The Papua New Guineans were attempting to travel between two islands on their country's east coast on April 4 but they had engine problems and ended up "helplessly drifting around parts of the Pacific Ocean", PNG's Post Courier newspaper said.
The four men, seven women and three children were seen off the Solomons, more than 1,000 kilometres southeast of PNG, by a sea plane on Tuesday, PNG's High Commissioner in the Solomon Islands Fred Yakasa said.
"I think the people back at home, they probably have assumed they are lost for good ... It's a long time at sea."
He gave no other precise details about where they were found or the boat they were on.
Yakasa said the survivors threw the body of the dead woman, believed to be in her late 40s or early 50s, overboard after waiting two days. They survived the ordeal by eating betel nut skins they had on board, he added.
Its users, which can be recognised by their red-stained teeth and lips, sing its praises as a pick-me-up that increases alertness, boosts energy and freshens the breath.
The PNG High Commission was arranging for the survivors to return home after getting the all-clear from doctors, the Post-Courier added.
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