Klubi Sportiv Besa Kavajë was first established in the municipality of Kavajë in October 1925 and originally operated under the name Shoqata Adriatiku. The team made their first appearance in the Albanian Superliga in 1933 and began using their current name in the same year. Throughout history, they have occasionally challenged for major honours at domestic level, especially in recent seasons. In the division's all-time league table they are currently ranked 7th.
In the 1971–72 season, the team reached the final of the Albanian Cup, where they eventually lost to Vllaznia Shkodër. Despite the loss, their performances in the competition granted them their first opportunity in a major UEFA competition, as they qualified for the UEFA Cup Winners' Cup. They made a promising start to their first European odyssey, beating the Danish side, Fremad Amager, on away goals. Unfortunately, in the following round, they were eliminated by Scottish club, Hibs.
To date, the club have never won the Superliga, although they did finish as runners up in both 1958 and 2009–10. In recent times, however, they have started to add silverware to their trophy cabinet. In 2007 and 2010, Besa Kavajë lifted the Albanian Cup, while 2010 also saw them win the Albanian Super Cup for the first time. As a result of this new-found level of success, the club have also made further forays into UEFA competitions in the last few years.
Dashamir Bajaziti and Daniel Xhafa are two of the most notable players to have worn the Besa Kavajë jersey and, during their respective spells with the side, both players were able to finish seasons as the overall Superliga top scorer.
The team's home matches are played at Besa Stadium, known as Stadiumi Besa in Albania, which is officially operated by the country's Football Association. The venue is currently able to hold a maximum of 9,000 spectators.