KÍ won the inaugural edition of Faroese top-tier football in 1942. In 1992, KÍ Klaksvík participated for the first time on a European stage, competing in the Champions League preliminary round against Skonto Riga of Latvia, where they lost 6–1 on aggregate.
By winning the double in 1999, KÍ reached a total of 17 league titles, a record at the time. KÍ didn't win the league title again until 2019, and although it held the honour of having won the most league titles since the 1950s, it was surpassed by HB in 2004. Although the team signed former great Todi Jónsson and local Atli Danielsen in July 2009 for the remainder of the season, KÍ was relegated for the first time in the club's 105 year-long history at the time.Despite a slow start, they managed to return to the top league for 2011, when they finished fifth under the guidance of manager Aleksandar Ðorđević.
In 2012, KÍ did one better than the previous year, and finished in 4th position. The team was the most potent attacking side, scoring 59 goals in 27 matches; Páll Klettskarð scored 22 goals and was the joint top-scorer. In the buildup to the 2013 season, Atli Danielsen and Meinhardt Joensen were signed, helping KÍ to reach the semi-final of the cup. However, they finished the league season in a disappointing 8th place. Ndende Adama Guéye was signed after the season, and the team hired a new manager, Mikkjal Thomassen, who has managed the team until the present. The new manager implemented a new system, foreign to most of the players, and so KÍ experienced a difficult start to the season. Later in the first half of the season, the team had implemented the style, playing attractive, free-flowing attacking football, eventually finishing fifth. In 2016, they missed out on their first league title since 1999 by just one point to Víkingur Gøta, although they did win the Faroe Islands Cup. The next year, they lost the title to the same team by an even closer margin, only having a slightly worse goal difference. While the next season was a disappointment, with the team only finishing fifth, the following years, starting with the 2019 season would prove remarkable ones.
That year, KÍ not only won their first title in twenty years, but they managed to reach the second qualifying round of the UEFA Europa League for the first time, defeating Riteriai from Lithuania on away goals. In 2020, KÍ went one better, becoming the first Faroese team to qualify for the Europa League playoff round by beating Dinamo Tbilisi 6–1 in the third qualifying round, which KÍ had reached for the first time. This shock result, against a much larger and more prestigious European club, was watched by seventy percent of the Klaksvik population, and set up what was labelled 'the biggest game in their history' against the Irish club Dundalk F.C, which they lost 3–1.