When will a new cycle's sunspots appear? We demonstrate a novel physical mechanism, namely, that a "solar tsunami" occurring in the Sun's interior shear-fluid layer can trigger new cycle's magnetic flux emergence at high latitudes, a few weeks after the cessation of old cycle's flux emergence near the equator. This tsunami is excited at the equator when magnetic dams, created by the oppositely-directed old cycle's toroidal field in North and South hemispheres, break due to mutual annihilation of toroidal flux there. The fluid supported by these dams rushes to the equator; the surplus of fluid cannot be contained there, so it reflects back towards high latitudes, causing a tsunami. This tsunami propagates poleward at a speed of 300 m/s until it encounters the new cycle's spot-producing toroidal fields in mid-latitudes, where it perturbs the fields, triggering their surface-eruption in the form of new cycle spots. A new sunspot cycle is preceded for several years by other forms of high-latitude magnetic activity, such as coronal bright points and ephemeral regions, until the tsunami causes the birth of new cycle's spots. The next tsunami is due by 2020, portending the start of intense `space weather' that can adversely impact the Earth.