In 1965, the municipality covered 79.8 square kilometres (30.8 sq mi), mostly islands and a small area on the mainland.

It encompassed part of what is now Kvinnherad Municipality (in Vestland county) and Vindafjord Municipality (in Rogaland county), primarily the islands of Fjelbergøya, Borgundøya, and Halsnøya, as well as some surrounding areas on the mainland.

On 1 January 1898, the southern part of the island of Huglo (population: 117) was transferred from Fjelberg to the neighboring Stord Municipality.

[4] The municipality (originally the parish) is named after the island of Fjelbergøya (Old Norse: Fjǫlbyrja) since the first Fjelberg Church was built there.

[6] The municipal council (Heradsstyre) of Fjelberg was made up of 21 representatives that were elected to four year terms.