The radiative decay of double K-shell vacancies in zirconium (Z=40), molybdenum (Z=42), and palladium (Z=46) was observed using a high-resolution transmission crystal spectrometer. The samples were ionized by the impact of 100-MeV $^{4}\mathrm{He}^{2+}$ ions. From the well resolved ${\mathit{K}}^{\mathrm{\ensuremath{-}}2}$\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{\ensuremath{-}}1}$${\mathit{L}}^{\mathrm{\ensuremath{-}}1}$ transitions, the energies, linewidths, intensity ratios, and double K-shell ionization cross sections were deduced. The experimental energies and linewidths of the hypersatellites are compared with results of Dirac-Hartree-Slater calculations and with multiconfiguration-Dirac-Fock calculations, both taking into account the Breit interaction. For the extracted double K-shell ionization cross sections a comparison is made with the semiclassical approximation predictions within the independent-particle model.