It was founded in 1903 as Knattspyrnufélag Vestmannaeyja by Björgúlfur Ólafsson, military doctor for the Dutch army.

ÍBV men's football team has won the Icelandic championship three times, in 1979, 1997 and 1998.

ÍBV women's football team has played in the top-tier Úrvalsdeild kvenna since 2011.

[6] On 24 December 2018, the team's goalkeeper, Kolbeinn Aron Arnarson, died at his home at the age of 29.

[7][8] ÍBV women's handball team has won the national championship four times, in 2000, 2003, 2004 and 2006.