From what I remember on the subject the depression ended because the New Deal had run its course with regards to money being spent and courts overturning FDR’s “laws” before WWII broke out.
In his book Rethinking the Great Depression (Chicago: Dee, 2002), Gene Smiley argues that the Depression actually continued well into the 1940's and contends that those who would otherwise be unemployed were in uniform, which created an illusion of prosperity. He argues that the Depression didn't really end until the government downsized itself after the war, when much of the New Deal and the wartime regulatory agencies were scrapped.