A link between the Atlantic Multidecadal Oscillation (AMO) and multidecadal variability of the Indian summer monsoon rainfall is unraveled and a long sought physical mechanism linking Atlantic climate and monsoon has been identified. The AMO produces persistent weakening (strengthening) of the meridional gradient of tropospheric temperature (TT) by setting up negative (positive) TT anomaly over Eurasia during northern late summer/autumn resulting in early (late) withdrawal of the south west monsoon and persistent decrease (increase) of seasonal monsoon rainfall. On inter--annual time scales, strong North Atlantic Oscillation (NAO) or North Annular mode (NAM) influences the monsoon by producing similar TT anomaly over Eurasia. The AMO achieves the interdecadal modulation of the monsoon by modulating the frequency of occurrence of strong NAO/NAM events. This mechanism also provides a basis for explaining the observed teleconnection between North Atlantic temperature and the Asian monsoon in paleoclimatic proxies.