The four-member squad conducted a "contact" search, sectioning off the area using a line attached to buoys.
Due to the poor visibility under the water, the search was conducted by touch.
The body was quickly located among the reeds near the lake's edge as the squad retraced their steps to the shore.
Senior Constable Peter Cunningham said it was likely the body had been further out in the lake but had drifted towards the shore some time in the past week.
A post-mortem examination and coroner's inquest would need to be completed before the cause of death could be confirmed, Mr Cunningham said.
"It's a long process, unfortunately - normally we would get someone to identify the person."
It was a relief that a body had been found and some closure could be given to family, Mr Cunningham said. At this stage there was no indication of any suspicious circumstances.
Searches using a helicopter and victim-recovery dogs had found no trace of the missing man. Last Sunday, a full-day operation involving about 20 police officers and search and rescue volunteers scoured the bush to a 100m elevation, but also found nothing.
Speaking shortly before the body was found, Mr Cunningham said he hoped the mystery of the disappearance would be resolved soon. "You get nothing, nothing, and then all of a sudden you get one thing that leads you to something. We've got to find them and you want the family to get them back."
Police said Mr Morris had no family in Wairarapa but had extended family in Wellington.