An autopsy revealed Mr Round had been beaten about the head, causing multiple skull fractures, and died in the evening of the day before he was found.
Mr Round spent much of his career as a news agency journalist for the New Zealand Press Association (NZPA) and Reuters.
He was one of the last New Zealand journalists to leave Saigon as the Vietnam War came to an end and later became Asia correspondent for NZPA in the 1970s.
Later roles at NZPA included political editor at the parliamentary press gallery, London bureau chief and editor - a role he held from 1984 to 1989.
The officer in charge of the murder investigation has welcomed the guilty plea.
Detective Senior Sergeant David Kirby of Whanganui police said it was "positive progress'' for Mr Round's family.
He declined to comment further until after sentencing.