I've loved this style for a long time but didn't know a name for it until recently.
It's primarily credited to UPA, or the United Productions of America, a 50s cartoon studio. It's a lot of bold graphic forms, more interested in feeling than realism, seemingly sort of in opposition to the Disney studio's strive for realism and in conversation with the Modern Art movement and contemporary artists of the time like Kandinsky and Mondrian.
It's kind of hard to find any definitive information about the studio online—there seem to be a couple good books that I've gotta check out—but there's a nice primer from Indiana University: