The club was founded as
Gosi on 25 December 1951 and was one of the founding members of the
Icelandic men's top division. On 22 December 1957 the club changed its name to
Körfuknattleiksfélag Reykjavíkur (English: Reykjavík Basketball Club) and played under that name until 1970. On 3 October 1970 the club merged into
Valur sports club and became its basketball department. Under the new name, Valur had considerable success in the 1980s, winning the Icelandic championship two times, in 1980 and 1983, and the Icelandic cup three times, 1980, 1981 and 1983. In 1992, Valur reached the Úrvalsdeild finals where it lost to
Keflavík 2–3. In 2022, Valur won its third national championship after beating
Tindastóll in the Úrvalsdeild finals. On 2 October 2022, Valur won its first
Super Cup, after defeating Icelandic Cup holders
Stjarnan 80–77. On 14 January 2023, Valur won its fourth
Icelandic Cup title, and its first in 40 years, after defeating
Stjarnan in the Cup final. ==Honours==