Latta, who attended Waitaki Boys' High School as a youth, shared the news in a video posted to Facebook on Thursday.
He said he was diagnosed a month ago after going to his GP complaining of a "really uncomfortable, sort of full feeling at the back of my throat".
He was then sent to a gastroenterologist, who found a tumour at the base of his stomach.
"She said it was probably cancer. That was not a great moment."
Latta said the specialist had given him between six and 12 months to live. The cancer was both inoperable and incurable, he said.
"That was probably the most traumatic thing I've ever been through.
"I remember standing outside after he told me this thing, and not knowing what to do or where to go. I remember standing there and being utterly paralysed."
He went to a hotel that night, ate "lots of ice cream" and cried, he said.
Latta is known for presenting the true crime series Beyond the Darklands and the Politically Incorrect Parenting shows, as well as his books on the same topics. Most recently, he presented the TVNZ show You've Been Scammed.
Since his diagnosis, he has been undergoing chemotherapy, which he said made him feel tired and sick - "like taking a cheese grater to all of the active cells in your body".
The treatment had seen his tumour shrink by about 60 percent, he said.
He would start a new three-month round of chemotherapy today, and "then we will see where we are up to", he said.
He now says he expects his prognosis to be longer than a year.
“I’m pretty sure I’m going to be around for quite some time,” he said in a subsequent post.
In the video, Latta also paid tribute to his wife, Natalie Flynn, who had been there for him throughout his diagnosis and treatment.
He referred to her as "the centre of my world" and said he was struggling to think of leaving her alone.
