The monk parakeet (Myiopsitta monachus) is a successful invasive species that does not exhibit life history traits typically associated with colonizing species (e.g., high reproductive rate or long-distance dispersal capacity). To investigate this apparent paradox, we examined individual and population genetic patterns of microsatellite loci at one native and two invasive sites. More specifically, we aimed at evaluating the role of propagule pressure, sexual monogamy and long-distance dispersal in monk parakeet invasion success. Our results indicate little loss of genetic variation at invasive sites relative to the native site. We also found strong evidence for sexual monogamy from patterns of relatedness within sites, and no definite cases of extra-pair paternity in either the native site sample or the examined invasive site. Taken together, these patterns directly and indirectly suggest that high propagule pressure has contributed to monk parakeet invasion success. In addition, we found evidence for frequent long-distance dispersal at an invasive site (∼100 km) that sharply contrasted with previous estimates of smaller dispersal distance made in the native range (∼2 km), suggesting long-range dispersal also contributes to the species’ spread within the United States. Overall, these results add to a growing body of literature pointing to the important role of propagule pressure in determining, and thus predicting, invasion success, especially for species whose life history traits are not typically associated with invasiveness.