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The club's roots are found in Hajduk sports society's basketball section, which was established in 1945. After three years of mostly sporadic activity, in 1948, the club established its own organizational structure known as KK Hajduk, which was independent of sports society. In the next year, 1949, the club changed its name to KK Split.

After competing in the Yugoslav lower divisions for more than a decade, the club finally made it to the Yugoslav top-tier level Yugoslav First Federal League, for the 1963–64 season, and it stayed there until the breakup of Yugoslavia.

In 1967, the club adopted–for sponsorship reasons–the name Jugoplastika (Jugoplastika was a factory of clothing, accessories, and footwear products, made from thermoplastic materials and fiberglass; the original predecessor of AD Plastik), and kept it until the end of the 1989–90 season. In the next season, the club participated in the worldwide, national domestic, and European competitions, under the sponsorship of POP 84 (an Italian clothes company from Ancona).

KK Split is among the most successful clubs in European basketball history. They are, together with the first champions of the competition, Rīgas ASK, the only team to win the EuroLeague trophy three times in a row. In the years 1989, 1990, and 1991, the team, which was known back then as Jugoplastika and POP 84, with players like Dino Rađa, Toni Kukoč, Žan Tabak, Velimir Perasović and Zoran Savić, won the European top-tier level basketball trophy.

Apart from these successes, the club also reached the FIBA European Champions Cup final in 1972, and the FIBA European Cup Winners' Cup final in 1973. It lost both finals against the 1970s Italian League superpower Ignis Varese, and the Soviet Union League club Spartak Leningrad. KK Split also won back-to-back Korać Cup titles in 1976, against Chinamartini Torino, and in 1977, against Alco Bologna.