Before Sunday, he had last been seen leaving a hotel in the town of Kilkivan with his dog on 6 January. He ran into trouble when his car got stuck in dirt on a farm road.
Police said Mr Weber spent three days in the car before running out of water and setting off on foot. He then became lost but remained near a dam where he survived by “sleeping on the ground, drinking dam water and eating mushrooms”.
An extensive air and ground search was suspended after failing to find him, but local property owners and police were told to keep an eye out.
Local MP Tony Perrett and his wife were reported to have found Mr Weber on Sunday just 3km (1.9 miles) from where his car had been discovered, after searching their cattle farm.
“He was sitting under a tree near a dam waving at us,” Mr Perrett told ABC.
“We’d been past this dam on numerous occasions over the last week and when we saw him there it was just quite extraordinary,” he added.
Mr Weber’s dog has not been found.