The northern terminus is at the North Dakota border as a continuation of North Dakota Highway 3, and runs south to South Dakota Highway 44 and South Dakota Highway 50 at Platte.

The southern terminus was at the intersection of present-day SD 50 and County Road 49 (CR 49) and the northern terminus was at the intersection of SD 10 in Leola.

By 1932, it was extended south along what was part of SD 47 to Wheeler.

In the early 1950s, when US 281 was relocated several miles to the east, SD 45 was extended back south to SD 50.

The north end of the route has remained in its current configuration since 1936.