Founded in 1925, Budućnost was the Montenegrin club with most appearances in the Yugoslav First League, debuting in 1946. Due to the city being renamed during communist rule in Yugoslavia, Budućnost was known as Budućnost Titograd throughout that era. Since Montenegrin independence in 2006, the club has won two Montenegrin First League titles and one Montenegrin Cup. They have also qualified for the UEFA Europa League and UEFA Champions League, but have never reached the group stage of either tournament.
Budućnost played in the Rapan Cup (Intertoto Cup) in 1981, when they came first in their group. They would go on to play in the Intertoto Cup in 1995 and in 2005. The most notable achiviement of the club on the international stage was reaching the final of the Balkans Cup in 1991 which they lost to FC Inter Sibiu, after being eliminated by Galatasaray S.K. in the previous round. Another notable result was the 2–1 win over Deportivo La Coruña in the Intertoto Cup in 2005.
Budućnost has enjoyed greater success since Montenegrin independence in 2006, finishing second three times and winning the 2007-08 and 2011-12 Montenegrin First League. The club has also reached three Montenegrin Cup finals (2007–08, 2009–10 and 2012–13), losing the first two appearances but winning the third time against Čelik Nikšić 1-0.
As a Yugoslav club Budućnost participated twice in the UEFA Intertoto Cup (1995 and 2005). Following independence, their first UEFA Cup season was in 2007-08, falling in the first qualifying round to Croatian club Hajduk Split. Budućnost qualified for their first UEFA Champions League the following season, and were eliminated at the same stage by Finns Tampere United. In the 2009-10 Europa League, Budućnost were knocked out in the first qualifying round by Polonia Warsaw, but in the next season's Champions League they were eliminated by Danish club Brøndby IF after defeating FK Baku in the second qualifying round. In the 2012-13 Champions League qualifiers they played against Śląsk Wrocław but also got eliminated in the 1st round.
FK Budućnost plays its home games at the Stadion Pod Goricom, in Podgorica. Stadion Pod Goricom, with 17,000 seats, is also the largest football stadium in Montenegro and the home ground of the Montenegro national football team. The stadium's original capacity was about 15,000 spectators, which expanded to 17,000 with the addition of the north and south stands. An eastern stand is planned to be built soon, which will bring the stadium's capacity to over 20,000.
Unforgettable matches played at the Stadion pod Goricom are: