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The club was founded in 1965 as Körfuknattleiksfélag Ísafjarðar (KFÍ).

In March 1983, KFÍ finished first in its group in 2. deild karla and played Laugdælir, Breiðablik and Íþróttafélag Menntaskólans á Egilsstöðum (ÍME) in they playoffs for the 2. deild championship and promotion to 1. deild karla. According to the rules at the time, each team would play the other three once and the team with the best win–loss record would be crowned champions. KFÍ lost its first game to Breiðablik, 79–76, despite 29 points from Guðjón Már Þorsteinsson and 21 points from Jón Oddsson. In the second game, against Laugdælir, KFÍ scored the last 4 points of the game, winning 79–76, with Kristinn Kristjánsson scoring 23 points, Jón Oddsson 17 points and Guðjón Már Þorsteinsson 16 points. In the final game, KFÍ defeated ÍME 91–70. Both Breiðablik and Laugdælir also won two out of three games, tied with KFÍ. As the rules did not count for any tie-breakers, the three teams were slated to meet again to decide the winner. During the second try, KFÍ lost to Breiðablik in the first game, 78–77, but won Laugdælir in the second game 79–76. Laugdælir however won Breiðablik leaving the teams again tied, thus meaning that a third playoff would be held to decide the winner. During the third playoff, KFÍ won Breiðablik but lost to Laugdælir. As Breiðablik won Laugdælir the teams were once again tied. Prior to the fourth playoffs, the Icelandic Basketball Federation decided that if the teams would once again finish tied, the team with the best scoring record would finish first. The fourth playoff was held from 30 April to 2 May and there Laugdælir won both KFÍ and Breiðablik convincingly and were crowned 2. deild karla champions.

In 1994, the team won the 2. deild karla playoffs, which was held jointly in Ísafjörður and Bolungarvík, after defeating Þór Þorlákshöfn 75–48, and was promoted to 1. deild karla.

On 17 October 1999, KFÍ won Skallagrímur, 129–132, in a game that went into four overtimes. It was the longest Úrvalsdeild karla game ever played in Iceland. Clifton Bush set a then record by playing 59 minutes in the game. It has since been broken by Hörður Axel Vilhjálmsson.

In 2016, KFÍ merged into Íþróttafélagið Vestri and became its basketball sub-division.

On 16 December 2018, while playing in the second-tier 1. deild karla, it knocked out top-tier Haukar in the Final 16 of the Icelandic Cup. It was the only team outside the top-tier Úrvalsdeild to appear in the Final 8 of the cup.

In June 2021, Vestri defeated Hamar in the 1. deild promotion finals and achieved promotion to the Úrvalsdeild.