Born and raised in Munich, Germany, Wuermer immigrated to the United States in 1915, settling in Chicago. He studied art at the Art Institute of Chicago from 1920 to 1924, then later studied with W.J. Reynolds, and finally at the Art Students League. Wuermer became known for his precisely rendered landscape paintings which utilized a painting technique similar to French pointillism.
Wuermer was active in the art community and was a member of the Grand Central Art Gallery, the Allied Artists of America, Hudson Valley Art Association, and the Woodstock Art Association.
Wuermer exhibited extensively throughout his career at venues such as the Art Institute of Chicago, the Salons of America, Corcoran Gallery, Buck Hill Falls Art Association, and solo shows at the Grand Central Art Gallery in 1930, 1934, 1938, and 1943. His works are found at Amherst College, Eleutherian Mills- Hagley Museum, High Museum of Art, IBM Corporation, Encyclopedia Britannica Collection of American Art, Royal Globe Company, London, and Syracuse University.