We predict by first-principles methods a phase transition in TiO2 at 6.5 Mbar from the Fe2P-type polymorph to a ten-coordinated structure with space group I4/mmm. This is the first report, to our knowledge, of the pressure-induced phase transition to the I4/mmm structure among all dioxide compounds. The I4/mmm structure was found to be up to 3.3% denser across all pressures investigated. Significant differences were found in the electronic properties of the two structures, and the metallization of TiO2 was calculated to occur concomitantly with the phase transition to I4/mmm. The implications of our findings were extended to SiO2, and an analogous Fe2P-type to I4/mmm transition was found to occur at 10 TPa. This is consistent with the lower-pressure phase transitions of TiO2, which are well-established models for the phase transitions in other AX2 compounds, including SiO2. As in TiO2, the transition to I4/mmm corresponds to the metallization of SiO2. This transformation is in the pressure range reached in the interiors of recently discovered extrasolar planets and calls for a reformulation of the equations of state used to model them.