Four influenza pandemics have struck the human population during the last 100 years causing substantial morbidity and mortality. The pandemics were caused by the introduction of a new virus into the human population from an avian or swine host or through the mixing of virus segments from an animal host with a human virus to create a new reassortant subtype virus. Understanding which changes have contributed to the adaptation of the virus to the human host is essential in assessing the pandemic potential of current and future animal viruses. Here, we develop a measure of the level of adaptation of a given virus strain to a particular host. We show that adaptation to the human host has been gradual with a timescale of decades and that none of the virus proteins have yet achieved full adaptation to the selective constraints. When the measure is applied to historical data, our results indicate that the 1918 influenza virus had undergone a period of preadaptation prior to the 1918 pandemic. Yet, ancestral reconstruction of the avian virus that founded the classical swine and 1918 human influenza lineages shows no evidence that this virus was exceptionally preadapted to humans. These results indicate that adaptation to humans occurred following the initial host shift from birds to mammals, including a significant amount prior to 1918. The 2009 pandemic virus seems to have undergone preadaptation to human-like selective constraints during its period of circulation in swine. Ancestral reconstruction along the human virus tree indicates that mutations that have increased the adaptation of the virus have occurred preferentially along the trunk of the tree. The method should be helpful in assessing the potential of current viruses to found future epidemics or pandemics.