The northern annular mode (NAM) influences wintertime climate variability in the Northern Hemisphere, and understanding the processes controlling its sign and amplitude is of critical importance. Mounting evidence supports a robust teleconnection between the El Niño–Southern Oscillation (ENSO) and the NAM, while internal variability generated in the tropical Indian Ocean (TIO) may be associated with a NAM response of the opposite sign. This study uses a coupled ocean–atmosphere model to separate the influence on the NAM from teleconnections driven by ENSO and the TIO. In composites constructed using a long preindustrial control integration, increased December–February precipitation in the central/eastern Pacific drives a negative late-winter NAM response. When isolated from ENSO variability, increased precipitation over the western-central TIO drives a strong and persistent positive NAM response throughout the winter. Opposite linear interference of the anomalous wave teleconnections explains most of the opposite-signed planetary wavedriving of the NAM responses. The case with combined ENSO and TIO variability yields cancellation of the wave interference and a weak NAM response. This mechanism is confirmed using experiments where the tropical ocean is nudged separately over the Pacific and TIO to the large-amplitude 1997/98–1998/99 ENSO cycle. The phases of the Rossby wave and NAM responses in these two cases are of opposite sign, providing strong evidence that internal variability over the TIO can induce teleconnections independent of—and with opposite sign to—those associated with ENSO.