Low precipitation enhances transmission of influenza viruses, which cause seasonal epidemics during the winter in northern and southern hemispheres. El Niño southern oscillation (ENSO) which modulates global precipitation is a multicomponent signal that is composed of sub-annual to multi-decadal oscillations. The dynamics of oscillatory components of ENSO and influenza are characterized, and causal relationship of annual oscillatory components is determined. Seasonality of influenza was determined in five geographical areas of north and south hemispheres. Monthly influenza time series of these regions and of ENSO were decomposed to oscillatory components. The oscillatory components were characterized in time-frequency and phase space domains. Periodicities of the oscillatory components of ENSO and influenza range from sub-annual to multidecadal. Time-dependent intrinsic correlations of instantaneous amplitude and frequencies of annual oscillatory components of ENSO and influenza are > 0.9. The dynamics of ENSO and influenza, which are dissipative with multifractal chaotic attractors, transit from quasi-periodic to chaotic regimes. Five most severe peaks of epidemic, which include 2009–2010 pandemic, occur during chaos. ENSO and influenza dynamics are phase coherent, but there is unidirectional causal effect of ENSO on influenza. Amplitude and frequency modulations of annual oscillatory components of ENSO and influenza are strongly coupled. Chaotic dynamics of ENSO determines the timing and severity of influenza epidemics. Monitoring of ENSO dynamics will aid public health surveillance of influenza epidemics.