Influenza A virus (IAV) is a major cause of morbidity and mortality throughout the world. Current antiviral therapies include oseltamivir, a neuraminidase inhibitor that prevents the release of nascent viral particles from infected cells. However, the IAV genome can evolve rapidly, and oseltamivir resistance mutations have been detected in numerous clinical samples. Using an in vitro evolution platform and whole-genome population sequencing, we investigated the population genomics of IAV during the development of oseltamivir resistance. Strain A/Brisbane/59/2007 (H1N1) was grown in Madin-Darby canine kidney cells with or without escalating concentrations of oseltamivir over serial passages. Following drug treatment, the H274Y resistance mutation fixed reproducibly within the population. The presence of the H274Y mutation in the viral population, at either a low or a high frequency, led to measurable changes in the neuraminidase inhibition assay. Surprisingly, fixation of the resistance mutation was not accompanied by alterations of viral population diversity or differentiation, and oseltamivir did not alter the selective environment. While the neighboring K248E mutation was also a target of positive selection prior to H274Y fixation, H274Y was the primary beneficial mutation in the population. In addition, once evolved, the H274Y mutation persisted after the withdrawal of the drug, even when not fixed in viral populations. We conclude that only selection of H274Y is required for oseltamivir resistance and that H274Y is not deleterious in the absence of the drug. These collective results could offer an explanation for the recent reproducible rise in oseltamivir resistance in seasonal H1N1 IAV strains in humans.