The present study focuses on the mechanism that controls the transition of the Euro-Atlantic circulation responses to the El Niño-Southern Oscillation (ENSO) from early (December) to late winter (February) for the period 1981-2015. A positive phase of ENSO induces a precipitation dipole with increased precipitation in the western and reduced precipitation in the eastern tropical Indian Ocean; this occurs mainly during early winter (December) and less so in late winter (February). It is shown that these inter-basin atmospheric teleconnections dominate the response in the Euro-Atlantic sector in early winter by modifying the subtropical South Asian jet (SAJET) and forcing a wavenumber-3 response which projects spatially onto the positive North Atlantic Oscillation (NAO) pattern. On contrary, during late winter, the response in the Euro-Atlantic sector is dominated by the well-known ENSO wave-train from the tropical Pacific region, involving extratropical anomalies that project spatially on the positive phase of the Pacific-North American (PNA) pattern and the negative phase of the NAO pattern. Numerical experiments with an atmospheric model (AGCM) forced by an Indian Ocean heating dipole anomaly support the hypothesis that Indian Ocean modulates the SAJET and enforces the Rossby wave propagation to the Euro-Atlantic region in early winter. These phenomena are also investigated using the ECMWF SEAS5 re-forecast dataset. In SEAS5, the ENSO inter-basin tropical teleconnections, and the response of the Euro-Atlantic circulation anomalies and their change from early to late winter are realistically predicted, although the strength of the early winter signal originated from the Indian Ocean is underestimated.