El Niño/Southern Oscillation (ENSO) is the largest natural interannual climate signal in the tropics; oscillations between warm El Niño and cold La Niña phases occur every few years. The effects are felt not only in the centre of action, the tropical Pacific region, but around the globe. Observational studies show a clear response in European climate to ENSO in late winter. However, the underlying mechanisms of the link are not yet understood. Here we use a general circulation model of the atmosphere, that has been extended into the upper atmospheric layers, to provide end-to-end evidence for a global teleconnection pathway from the Pacific region to Europe via the stratosphere. We present evidence for an active stratospheric role in the transition to cold conditions in northern Europe and mild conditions in southern Europe in late winter during El Niño years. In our experiments, this mechanism is restricted to years when stratospheric sudden warmings occur. The response in European surface climate to the El Niño signal is large enough to be useful for seasonal forecasting.