Monitoring changes in influenza A virus genomes is crucial to understand its rapid evolution and adaptation to changing conditions e.g. establishment within novel host species. Selective sweeps represent a rapid mode of adaptation and are typically observed in human influenza A viruses. We describe Sweep Dynamics (SD) plots, a computational method combining phylogenetic algorithms with statistical techniques to characterize the molecular adaptation of rapidly evolving viruses from longitudinal sequence data. To our knowledge, it is the first method that identifies selective sweeps, the time periods in which these occurred and associated changes providing a selective advantage to the virus. We studied the past genome-wide adaptation of the 2009 pandemic H1N1 influenza A (pH1N1) and seasonal H3N2 influenza A (sH3N2) viruses. The pH1N1 influenza virus showed simultaneous amino acid changes in various proteins, particularly in seasons of high pH1N1 activity. Partially, these changes resulted in functional alterations facilitating sustained human-to-human transmission. In the evolution of sH3N2 influenza viruses, we detected changes characterizing vaccine strains, which were occasionally revealed in selective sweeps one season prior to the WHO recommendation. Taken together, SD plots allow monitoring and characterizing the adaptive evolution of influenza A viruses by identifying selective sweeps and their associated signatures.