Fluorohypsum is a solid, large-tonnage waste generated during the production of hydrofluoric acid. The volume of accumulated waste in the world is hundreds of millions of tons, which makes its utilization an increasingly urgent task. This article presents the results of research aimed at the use of fluorohypsum as a component of building materials. On the basis of the obtained data, the technological scheme of manufacturing products based on anhydrite binder is developed. It was established that the introduction of specialized additives into gypsum–anhydrite mixtures significantly increases the bond strength with the base (up to four times). The mixture of gypsum and anhydrite with a 75/25 arrangement provides tensile strength of up to 4.3 MPa and bending strength of 1.8 MPa, which exceeds similar indicators for traditional building materials. An economic analysis has shown a 20–25% reduction in the cost of composite production compared to the use of natural gypsum, which provides cost savings and makes these materials competitive.