Achromatic doublets are combinations of two individual lenses designed to focus different wavelengths of light in the same position. Apochromatic optics are improved versions of the achromatic schemes which extend the wavelength range significantly. Both achromatic and apochromatic optics are well-established for visible light. However, X-ray achromatic lenses did not exist until very recently, and X-ray apochromatic lenses have never been experimentally demonstrated. Here, we create an X-ray apochromatic lens system using an appropriate combination of a Fresnel zone plate and a diverging compound refractive lens with a tuned separation distance. The energy-dependent performance of this apochromat was characterized at photon energies between 6.5 and 13.0 keV by ptychographic reconstruction of the focal spot and scanning transmission X-ray microscopy of a resolution test sample. The apochromat delivered a reconstructed focal spot size of 940 × 740 nm2. The apochromatic combination shows a four-fold improvement in the chromatic aberration correction range compared to an achromatic doublet configuration. Thus, apochromatic X-ray optics have the potential to increase the focal spot intensity for a wide variety of X-ray applications.