The structures of krypton and xenon single crystals have been determined by X-ray diffraction at low temperatures. Both noble gases were crystallized by in situ crystallization techniques and found in a face-centered cubic (fcc) type structure. The electron density was reconstructed in both crystals from the X-ray structure amplitudes. It was calculated by full-potential LAPW method at the experimental geometry. A topological electron density analysis and the deformation electron density maps have shown that both Kr and Xe atoms are contracted in the solid state relative to the free atoms and are slightly aspherically polarized to each other, with bridges directed along atom-atom lines. The critical point characteristics indicate the closed-shell interactions in both crystals.