WELLINGTON, New Zealand—The final four designs for New Zealand’s proposed new national flag were revealed Tuesday.

For more than a century, New Zealanders have fought wars and won Olympic medals under a flag with four red stars on a blue background and Great Britain’s Union Jack in the corner. The stars, arranged in a Southern Cross formation, indicated New Zealand’s location in the South Pacific while the incorporation of the Union Jack harked back to the island nation’s time as a British colony.

Now,...