Influenza A virus (IAV) has a segmented genome that allows for the exchange of genome segments between different strains. This reassortment accelerates evolution by breaking linkage, helping IAV cross species barriers to potentially create highly virulent strains. Challenges associated with monitoring the process of reassortment in molecular detail have limited our understanding of its evolutionary implications. We applied a novel deep sequencing approach with quantitative analysis to assess the in vitro temporal evolution of genomic reassortment in IAV. The combination of H1N1 and H3N2 strains reproducibly generated a new H1N2 strain with the hemagglutinin and nucleoprotein segments originating from H1N1 and the remaining six segments from H3N2. By deep sequencing the entire viral genome, we monitored the evolution of reassortment, quantifying the relative abundance of all IAV genome segments from the two parent strains over time and measuring the selection coefficients of the reassorting segments. Additionally, we observed several mutations coemerging with reassortment that were not found during passaging of pure parental IAV strains. Our results demonstrate how reassortment of the segmented genome can accelerate viral evolution in IAV, potentially enabled by the emergence of a small number of individual mutations.