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Sir Des was well known for his 1970s television cooking show and was one of the country's first celebrity chefs.
He was Wellingtonian of the Year in 2011, having been the City Missioner from 1994 until then. He was knighted in 2012.
Wellington Mayor Andy Foster said the city was mourning the loss of Sir Des.
"Sir Des was a giant of the Wellington community and his passing leaves a huge gap in our city."
"In his 17 years leading the Mission it grew in size and importance to our city and demonstrated the care we should take for each other," he said.
"Rest in peace, Sir Desmond," Foster said.
Current Wellington City Missioner Murray Edridge said Sir Des would be deeply missed.
"He set the standard - he did it with vitality and energy and flamboyance - and he's remembered for the contribution he made and the compassion he had for people."
Sir Des was ordained as an Anglican minister in 1983 and was the vicar of St Barnabas in Roseneath.
His wife Lorraine died last year, and he is survived by their daughter Debra and son Dominic.