Nietzsche does not say, "There is no God," or "I do not believe in God," but "God is dead." He believes that he is ascertaining a fact of present-day reality when he peers clairvoyantly into his age and his own nature.In other words, "we're all atheists now". Or as Nz puts it "atheism is the only honest air we breathe, we more spiritual men of today"*.
I've been dipping in and out of Karl Jaspers' book on Nietzsche. Why God died is a more difficult question and Jaspers takes a number of pages to explore it.