Since its maiden voyage to Tahiti in 1976, using only traditional navigation and sailing techniques, it has completed nine other major voyages through Polynesia, Micronesia, Japan, Canada and the United States.
In May 2014 the Hokulea set sail on its most ambitious voyage - a three-year circumnavigation of the world where it will cover 47,000 nautical miles with stops at 85 ports in 26 different countries.
One of those ports will be Napier, and Mr Smith said the Voyaging Trust as well as local iwi will put on "a special welcome for a special occasion".
The waka is presently in Auckland and the original voyage plans had it sailing for Wellington, then a top of the South Island call, before returning up the eastern seaboard to Napier.
"But they are constantly having to change their plans due to the weather - so once they leave Auckland they will be heading here."
Mr Smith said the waka was traditional to the point of not having an auxiliary engine, like Te Matau a Maui, so was more susceptible to weather.
The exact time of arrival was therefore still up in the air, but he was in constant contact with the crew and believed it was likely to be around Tuesday or Wednesday.
"Once they get around East Cape we'll have a better idea."
Mr Smith said as it has no engine and requires towing in and out of harbours the Hawke's Bay Coastguard had stepped up to say they would assist in that role.
The Napier City Council and the Napier Sailing Club had also assisted by arranging moorings for the waka and its support boat.
It will be in Napier for about a week with the seven Hawaiian crew and four guest crew members staying at the Kohupatiki Marae in Clive.
Members of the trust said they were privileged to host the waka as it was uncertain when, and if, it would ever return.