Curran was born in Hartford, Kentucky; however, the family moved to Sandusky, Ohio, on the shore of Lake Erie, after the start of the Civil War. He first studied at Cincinnati School of Design before moving to New York City in 1882, where he studied at the National Academy of Design, under Walter Satterlee, then at the Art Students League. He spent the years circa 1889 to 1891 in Paris, France in study at the Academie Julian under Benjamin Jean-Joseph Constant; Jules-Joseph Lefebvre; and Henri-Lucien Doucet. Curran returned to New York City in 1891, where he maintained an apartment and studio, but also spent summers in Ohio to visit family and to sketch and paint. Upon an invitation by artist Frederick Dellenbaugh in 1903, Leigh visited the Cragsmoor Art Colony, located in the dramatic landscape of the Shawangunk Mountains within the Hudson River system. It was to become his summer home for nearly forty years and where he painted his subjects against the backdrop of the mountains. The following year, Curran began teaching at the National Academy of Design; Pratt Institute Art School; and the Cooper Union Art School, Cooper School of Design. Curran was a member of the American Watercolor Society, Painters in Watercolor; Brooklyn Art Association; National Arts Club, New York; Salmagundi Club; Boston Art Club; National Academy of Design; New York Water Color Club, Society; and the Society of American Artists. Curran exhibited at the National Academy of Design; American Watercolor Society, Painters in Watercolor; Brooklyn Art Association; National Academy of Design; Society of Washington Artists, DC; Art Institute of Chicago; Boston Art Club; Lotos Club; Salmagundi Club, New York City; World’s Columbian Exposition, Chicago (1892-1893); Louisiana Purchase Expo, St. Louis World’s Fair (1904); Art Institute of Chicago; The Pennsylvania Academy of the Fine Arts. Curran was awarded prizes at the National Academy (1888, 1893,1895, 1919); Paris Salon (1890); Columbian Exposition, Chicago (1893); Atlanta Exposition (1895); Paris Exposition (1900); Pan-American Exposition, Buffalo, NY (1901, also the Assistant Director of the Expo.); Society of American Artists (1904); St. Louis Exposition (1904); Society of Washington Artists (1905) and the Salmagundi Club (1933).