The beginnings of the foundation of Te Umanibong date to 1971, when the intention was set after a UNESCO meeting in Suva . This led to the foundation in 1973 of the Tungavalu Society, which was set up by islanders and people in the diaspora from the Gilbert and Ellice islands.[ The society ran a newsletter called Banan Tungavalu, which was distributed from September 1974. In 1975, the society held their first exhibition and a craft competition.

In 1990 the government of New Zealand funded the construction of a museum building in Bikenibeu. In order for the museum to be built, a sea wall had to be constructed to drain and reclaim the land. The building opened in 1991 and raised the profile of the organisation both within the country and overseas. At the same time as the museum was being built, a mwaneaba was constructed in the grounds. There is also a botanic garden in the grounds, with a focus on medicinal plants.