Tonks served in the role between 1990 and 1995. He was also chairman of the International Rugby Board, now known as World Rugby.
In 2004, he was made a life member of NZ Rugby.
Current NZR chair Brent Impey says Tonks' service to the game was immeasurable.
"Eddie started on what was then the NZRFU Council in 1986, and played a key role in the organisation of the 1987 Rugby World Cup, which of course was a huge success. Nearly a decade later he helped lay the groundwork for the game to go professional in 1996.
"He was hugely respected in both business and rugby and will be missed. Our thoughts are with his wife Claire and their family."
NZR chief executive Mark Robinson says Tonks' was immense in his work.
"He served as Deputy Chair on the Wellington Rugby Football Union Board for more than a decade, held various positions at New Zealand Rugby for a similar period and went onto Chair the International Rugby Board.
"His record speaks for itself and he left the game in a better place than he found it."
Tonks took over the helm of NZR as the game was turning professional. He made the questionable call to appoint Sir John Hart as co-coach of the All Blacks ahead of the 1991 Rugby World Cup.
He also served as Deputy Chair of Wellington RFU from 1977 until 1989.
