During the 1960s, there were many municipal mergers across Norway due to the work of the Schei Committee.

It may come from the word mosi which means "mossy swamp", likely because the island is marshy.

It could also come from the word mostr which means "pleased" or "large amount", possibly referring to the fact that the island is very hilly.

The mayor was indirectly elected by a vote of the municipal council.

[6] The municipal council (Heradsstyre) of Moster was made up of 17 representatives that were elected to four year terms.