Paine was the only New Zealander to have served in World War I. His wife, Margaret, died in 2003 at the age of 87.
The New Zealand Press Association has said the funeral will be held in Auckland on Saturday.
Prime Minister John Key has said O’Neill was an “extraordinary” journalist.
O’Neill joined the Press Council in 1974 and worked as a journalist for the New Zealand Herald for 20 years.
He wrote the book The New Zealand of the 20th Century, which described New Zealand as a country that was “in the midst of a profound transformation”.
Owing to the country’s “crisis of identity”, O’Donnell said the book was written to “give voice to a new nation”.
“New Zealand has always been a country of difference and this is what makes it special,” O’Neil said.
“I was trying to find out how this new nation was emerging from the crisis of identity and I think we have all been wondering what we could do differently to help.”
The Press Council is a voluntary organisation that represents and encourages the press in New Zealand.
The Press Club has been established to honour and promote the profession of journalism.