A method of fabricating multilayer focusing mirrors that can focus X-rays down to 10 nm or less was established in this study. The wavefront aberration induced by multilayer Kirkpatrick-Baez mirror optics was measured using a single grating interferometer at a photon energy of 9.1 keV at SPring-8 Angstrom Compact Free Electron Laser (SACLA), and the mirror shape was then directly corrected by employing a differential deposition method. The accuracies of these processes were carefully investigated, considering the accuracy required for diffraction-limited focusing. The wavefront produced by the corrected multilayer focusing mirrors was characterized again in the same manner, revealing that the root mean square of the wavefront aberration was improved from 2.7 (3.3) rad to 0.52 (0.82) rad in the vertical (horizontal) direction. A wave-optical simulator indicated that these wavefront-corrected multilayer focusing mirrors are capable of achieving sub-10-nm X-ray focusing.