There are only a few hundred North Island kokako left, and the South Island kokako is thought to be extinct.
The five birds are to join 15 others which have been transferred to the island over the past two years.
Secretary Island is the only South Island destination in the project, chosen as a haven for the birds because of its extensive predator control.
The Fiordland Lobster Company has invested about $80,000 in the past two years in capturing and transferring the birds.
Chief executive Mike Schuck said the company wanted to help the environment in which it operated.
"We want to do something positive for Fiordland and for the fishermen who live and work there.
"Fiordland is a place of incredible natural beauty and our fishermen have a real passion for it."
It was not the first time the company had sponsored environmental projects in the region - in 2005 it donated $15,000 to eradicate stoats from Pigeon Island and Dusky Sound.
However, Mr Schuck said the company was not doing it for commercial reasons: "It's about giving back to Fiordland".
The Department of Conservation hoped the Secretary Island birds would begin breeding next year.
