During the 1930s, Sweden acquired an assortment of different submachine guns, including Bergmanns, Thompsons, and Suomis. As World War Two progressed, they decided that they really needed to standardize on a single caliber and model of gun, and requested designs from both the Carl Gustav factory and Husqvarna. The Carl Gustav design won out, and was adopted as the m/45.

It was a very simple open-bolt, tube-receiver, fixed-firing-pin design chambered for 9x19mm Parabellum ammunition. The original guns were built around Finnish Suomi magazines, both 71-round drums and 50-round "coffin" mags. After the war these were replace by a new 36-round traditional box magazine, and magazine well adapters were fitted to the guns which precluded the use of the larger mags. The new magazines were much more convenient to carry, less expensive, and more reliable.

The name "Swedish K" comes form the full designation: Kulsprutepistol m/45. The guns were used by American special operations forces in Vietnam until the Swedish government stopped export sales to the US, at which point the Navy commissioned Smith & Wesson to produce the Model 76 submachine gun (essentially a copy of the m/45). The design was also licensed by Egypt, which also licensed the AG-42 Ljungman rifle at the same time. The Egyptian copy was called the Port Said, and shows the features fo the original Swedish m/45 pattern, where the guns in Swedish service were mostly updated to the m/45B pattern.