Cook's legacy has been divisive in the town, which is roughly half Pākehā and half Māori.
The explorer first made landfall in Poverty Bay in 1769, and his crew killed nine iwi members from Ngāti Oneone after a misunderstanding.
Another Cook statue was removed from Kaiti Hill overlooking Gisborne last year, as part of the 250th commemorations of Cook's arrival.
The maunga was sacred to Ngāti Oneone, and the monument depicting Cook as heroic was insulting, the iwi said.
New sculptures now stand in its place, and the original statue is being moved to the grounds of Tairāwhiti Museum.
The Gisborne District Council recently reversed a decision to install two Endeavour replicas in the town centre after an outcry by iwi, who said they were not consulted.
Statues around the world have been removed, torn down and defaced as part of protests against racial injustice which were sparked by the death of African American George Floyd in Minneapolis.
