The son of a German painter of interior decorations, Louis Moeller worked as his father's apprentice for three years. Further study took place in the early 1870s at the Cooper Union (evenings) and the NAD Antique School (days). By 1873, Moeller had left for Munich where he studied with Wilhelm von Diez and Frank Duveneck. He apparently remained abroad for a number of years, returning to New York in the early 1880s. For financial reasons, Moeller worked briefly as a decorative painter, but his painstakingly rendered genre paintings soon established his reputation. Moeller's Puzzled won the First Hallgarten Prize in 1884, the initial conferral of the award. The ensueing popularity of his work was no doubt a partial result of the patronage of the influential Thomas B. Clarke, who owned more works by Moeller than by any other artist. His paintings were often compared to those of Charles Ulrich, Charles X. Harris, and Richard Creifelds.
After moving to Mount Vernon, New York in 1894, Moeller lived quietly while demand for his work diminished. In 1917, after the death of his wife, Marianne von Brandeis, he moved to New Jersey to live with his brother-in-law. During the final years of his life, illness prevented him from working. Shortly before his death, he signed over his estate to a home for the elderly in North Bergen, New Jersey.