An H1N1 subtype influenza A virus with all 8 gene segments derived from wild birds (including mallards), ducks and chickens, caused severe disease outbreaks in swine populations in Europe beginning in 1979 and successfully adapted to form the European avian-like swine (EA-swine) influenza lineage. Genes of the EA-swine lineage, that are clearly segregated from its closest avian relatives, continue to circulate in swine populations globally and represent a unique opportunity to study the adaptive process of an avian to mammalian cross-species transmission. Here, we used a relaxed molecular clock model to test whether the EA-swine virus originated through the introduction of a single avian ancestor as an entire genome, followed by an analysis of host-specific selection pressures among different gene segments. Our data indicated that independent introduction of gene segments via transmission of avian viruses into swine followed by reassortment events that occurred at least 1–4 years prior to the EA-swine outbreak. All EA-swine gene segments exhibit greater selection pressure than avian viruses, reflecting both adaptive pressures and relaxed selective constraints that are associated with host switching. Notably, we identified key amino acid mutations in the viral surface proteins (H1 and N1) that play a role in adaptation to new hosts. Following the establishment of EA-swine lineage, we observed an increased frequency of intra-subtype reassortment of segments compared to the earlier strains that has been associated with adaptive amino acid replacements, disease severity and vaccine escape. Taken together, our study provides key insights into the adaptive changes in viral genomes following the transmission of avian influenza viruses to swine and the early establishment of the EA-swine lineage.