The tectonic evolution of the Arctic Region in the Mesozoic and Cenozoic is considered with allowance for the Paleozoic stage of evolution of the ancient Arctida continent. A new geodynamic model of the evolution of the Arctic is based on the idea of the development of upper mantle convection beneath the continent caused by subduction of the Pacific lithosphere under the Eurasian and North American lithospheric plates. The structure of the Amerasia and Eurasia basins of the Arctic is shown to have formed progressively due to destruction of the ancient Arctida continent, a retained fragment of which comprises the structural units of the central segment of the Arctic Ocean, including the Lomonosov Ridge, the Alpha-Mendeleev Rise, and the Podvodnikov and Makarov basins. The proposed model is considered to be a scientific substantiation of the updated Russian territorial claim to the UN Commission on the determination of the Limits of the Continental Shelf in the Arctic Region.