John said he was first alerted that his son was okay via a Facebook post, and has since talked to his son.
He said he didn't discuss with his son where he had been or what he was doing but said "everything was well".
He added his son may be returning to Australia on Wednesday.
Cooke's parents became increasingly worried as time passed without word from him.
Immigration New Zealand told them their son had entered New Zealand, but he wasn't heard from after he landed.
Cooke had travelled extensively internationally and within Australia and always touched base to let his parents know what he was doing when he arrived somewhere, his father John earlier told the Herald.
It was unclear where in New Zealand Cooke was travelling to, but it was likely he had come to sell strawberries, a job he had been doing in Australia for the last six to nine months.
He had never been to New Zealand before, John said, but was supposed to be meeting up with a friend when he arrived.
Last Friday police appealed for any sightings of Cooke.