The positive phase of the El Niño-Southern Oscillation (ENSO) increases global mean temperature, and contributes to a negative phase of the Southern Annular Mode (SAM), the dominant mode of climate variability in the Southern Hemisphere. This interannual relationship of a high global mean temperature associated with a negative SAM, however, is opposite to the relationship between their trends under greenhouse warming. We show that over much of the 20th century this relationship undergoes multidecadal fluctuations depending on the intensity of ENSO. During the period 1925-1955, subdued ENSO activities weakened the relationship. However, a similar weakening has occurred since the late 1970s despite the strong ENSO. We demonstrate that this recent weakening is induced by climate change in the Southern Hemisphere. Our result highlights a rare situation in which climate change signals emerge against an opposing property of interannual variability, underscoring the robustness of the recent climate change.