Nonlinear integrations with a 3-D primitive equation model of the middle and upper atmosphere reveal global-scale Kelvin waves. Owing to their meridional extent, these eastward propagating disturbances can be excited by tropospheric fluctuations over much of the globe. Stochastic forcing in the midlatitude troposphere produces an eastward response that involves the Kelvin normal mode, with barotropic vertical structure, as well as a continuum of vertically propagating Kelvin waves. Having periods of order a day and shorter, those disturbances are all global. Transient fluctuations representative of midlatitude weather systems reproduce observed Kelvin structure and amplitude near the tropopause. Vertical amplification then leads to wind fluctuations at mesospheric and thermospheric altitudes of 5--15 m/s. Approaching tidal amplitudes, global Kelvin waves should therefore represent a measurable if not prominent feature at those altitudes.