Prime Minister John Key said New Zealand had lost a "remarkable New Zealander".
At the Domingo concert last week, Mr Key said Mr Doig's commitment to cricket, rugby and the city of Christchurch was "truly breathtaking".
Mr Doig was on the board of the New Zealand Rugby Union, and was involved with Sparc, CreativeNew Zealand and New Zealand Rowing.
Sparc chief executive Peter Miskimmin said Mr Doig was one of very few people to bridge the gap between the arts and sport.
"We have lost one of the truly great, inspirational New Zealanders."
Rugby Union chairman Mike Eagle said Mr Doig's contribution to New Zealand through sports, art and entertainment was immense.
NZ Cricket chief executive Justin Vaughan said Mr Doig was a great servant of New Zealand Cricket and an "insightful and astute administrator".
Creative New Zealand chief executive Stephen Wainwright said Mr Doig was "in many ways a force of nature".
"His generosity was extraordinary and even during his illness he considered himself to be a fortunate man."
Born and educated in Christchurch, Mr Doig graduated from Canterbury University with a masters degree in English and went on to sing in major opera houses in Europe in a musical career lasting 25 years.
In 1995, he gave up fulltime singing to become New Zealand Cricket chief executive, a job he held until March 2001.
Mr Doig was made a Companion of the New Zealand Order of Merit in this year's Queen's Birthday Honours for services to the arts and sport.
The Christopher Doig Foundation was launched last week.
It was established to nurture and develop the leadership potential of outstanding young people.