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The boy, believed to be 20 months old, is being cared for by child services after a man walked into the Manukau Winz office at 2.20pm and handed him to staff.
Police said they had identified the man and located the boy's family after appealing for information earlier this afternoon.
"Police will now be working with CYF on the investigation and will not be making any further comment on the case," a police spokeswoman said.
The boy was wearing a white T-shirt, faded black denim shorts and a nappy when he was left at the WINZ office. He had with him a bag containing another pair of shorts, T-shirt and two long-sleeved tops.
Police said he was taken to Middlemore Hospital and found to be in good health.