The parish of Hordnæs og Iveland was established as a municipality on 1 January 1838 (see formannskapsdistrikt law).

[6] The two neighboring parishes of Hornnes and Iveland were put together as a single municipality after the formannskapsdistrikt law went into effect on 1 January 1838.

This is likely referring to the two horn-shaped peninsulas that jut out into the river Otra at the entrance to the lake Breidflå.

The first element is the genitive case of the local river name Ífa which now called the Frøysåna.

The river name is probably derived from the word ýr which means "yew" (Taxus baccata).