Current chairman Tony Porter said his board is "deeply saddened" by the death of Mr Story, who had been battling an illness for some time.
"Nick led the airport through a period of record growth and profit over his four-year tenure," Mr Porter said. "Nick always conducted himself with dignity and integrity and continued to work tirelessly after his diagnosis to ensure the company is in a very strong position ahead of the airport expansion project."
Mr Porter said the CEO had expanded the vision and the services at the airport, and added: "He was a strategic thinker and a strong leader, and was very well respected in the business community."
Napier Mayor Bill Dalton, whose city has a 26 percent shareholding in the Airport company - the Government has a half-share and the Hastings District Council 24 percent - said the success of Mr Story's time was the growth in airport traffic.
"He has been not only a very successful CEO of the airport company but also a very good citizen, as a Rotarian who has been involved in a number of projects," Mr Dalton said.
"He did a great job with the new airlines coming here, and lately with the expansion taking place at the airport. It's a huge project."
Holding a Bachelor of Commerce and Administration, with a Post Graduate Diploma in Marketing and a Master of Professional Studies, Mr Story had at the time of his appointment been most recently area manager East Coast for Westpac Business Banking.
He had previously held senior business development and marketing positions with several national organisations, including being general marketing manager at Farmlands and business development manager, global marketing and strategy at Fonterra.
Outside of his role at the airport he has been a director of Centralines Limited and a president of the Rotary Club of Hastings Karamu.
The son of Terry and Clare Story, he was one of seven siblings raised in Waipawa and later went to high school at St Patrick's College, Silverstream.
Survived also by wife Melissa and son Ben, his funeral will be held at Sacred Heart Catholic Church, Hastings, on Thursday, starting at 1pm.