In 1903, various university scientific collections were brought together and organized under the direction of Junius Henderson (1865–1937), who came to Colorado to be a lawyer and later became a county judge. His interest in the sciences led him to voluntarily help the university label its growing collection of fossils, shells, and minerals.
After his formal appointment as curator, Henderson established museum rooms in the Hale Building. After receiving a BA in natural history, he became a professor. In 1910, the museum collection moved to a new building, now the Geology Building. In 1937, a new museum was built with Public Works Administration money. It was named in Henderson's honor two years after his death.
The building shows Klauder's ability to design buildings of varying functions. Since the gallery spaces do not need windows, Klauder used the campus standard sandstone, cut in squares and laid flat. These stones, called "shiners," are used in place of windows on the lower floors. The museum lobby, with its elegant curved stair, is one of Klauder’s most impressive interior spaces. Glen Huntington was the associate architect on this project.