Several human pathogens exhibit distinct patterns of seasonality and circulate as pairs of discrete strains. For instance, the activity of the two co-circulating influenza A virus subtypes oscillates and peaks during winter seasons of the worlds temperate climate zones. These periods of increased activity are usually caused by a single dominant subtype. Alternation of dominant strains in successive influenza seasons makes epidemic forecasting a major challenge. From the start of the 2009 influenza pandemic we enrolled influenza A virus infected patients (n = 2,980) in a global prospective clinical study. Complete hemagglutinin (HA) sequences were obtained from 1,078 A/H1N1 and 1,033 A/H3N2 viruses and were linked to patient data. We then used phylodynamics to construct high resolution spatio-temporal phylogenetic HA trees and estimated global influenza A effective reproductive numbers (R) over time (2009-2013). We demonstrate that R, a parameter to define host immunity, oscillates around R = 1 with a clear opposed alternation pattern between phases of the A/H1N1 and A/H3N2 subtypes. Moreover, we find a similar alternation pattern for the number of global virus migration events between the sampled geographical locations. Both observations suggest a between-strain competition for susceptible hosts on a global level. Extrinsic factors that affect person-to-person transmission are a major driver of influenza seasonality, which forces influenza epidemics to coincide with winter seasons. The data presented here indicate that also cross-reactive host immunity is a key intrinsic driver of global influenza seasonality, which determines the outcome of competition between influenza A virus strains at the onset of each epidemic season.