Born in Lübeck as the oldest child of Thomas Johann Heinrich Mann and Júlia da Silva Bruhns, he was the elder brother of Thomas Mann. His father came from a patrician grain merchant family and was a Senator of the Hanseatic city. After the death of his father, his mother moved the family to Munich, where Heinrich began his career as a freier Schriftsteller or free novelist.

His essay on Zola and the novel Der Untertan earned him much respect during the Weimar Republic, since it satirized German society and explained how its political system had led to the First World War. Eventually, his book Professor Unrat was liberally adapted into the successful movie Der Blaue Engel (The Blue Angel). Carl Zuckmayer wrote the script, and Josef von Sternberg was the director. The book's author wanted his girlfriend, the actress Trude Hesterberg, to play the lead, but Marlene Dietrich was given her first major role instead as Lola Lola the "actress" (named Rosa Fröhlich in the novel).

Together with Albert Einstein and other celebrities, Mann was a signatory to a letter to the International League of Human Rights condemning the murder of Croatian scholar Dr Milan Šufflay on 18 February 1931.

Mann became persona non grata in Nazi Germany and left even before the Reichstag fire in 1933. He went to France where he lived in Paris and Nice. During the German occupation he made his way to Marseille in Vichy France and there was aided by Varian Fry in 1940 to escape to Spain. He then went to Portugal and sailed to America.

During the 1930s and later in American exile, his literary career went downhill, and eventually he died in Santa Monica, California, lonely and without much money, just months before he was to move to Soviet-occupied Germany to become president of the Prussian Academy of Arts. His ashes were later taken to East Germany.

His second wife Nelly Mann (1898-1944) committed suicide in Los Angeles.

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