Guava (Psidium guajava) is an aggressive invasive plant in the Galapagos Islands. Determining its provenance and genetic diversity could explain its adaptability and spread, and how this relates to past human activities. With this purpose, we analyzed 11 SSR markers in guava individuals from Isabela, Santa Cruz, San Cristobal, and Floreana islands in the Galapagos, as well as from mainland Ecuador. The mainland guava population appeared genetically differentiated from the Galapagos populations, with higher genetic diversity levels found in the former. We consistently found that the Central Highlands region of mainland Ecuador is one of the most likely origins of the Galapagos populations. Moreover, the guavas from Isabela and Floreana show a potential genetic input from southern mainland Ecuador, while the population from San Cristobal would be linked to the coastal mainland regions. Interestingly, the proposed origins for the Galapagos guava coincide with the first human settlings of the archipelago. Through approximate Bayesian computation, we propose a model where San Cristobal was the first island to be colonized by guava from the mainland, and then, it would have spread to Floreana and finally to Santa Cruz; Isabela would have been seeded from Floreana. An independent trajectory could also have contributed to the invasion of Floreana and Isabela. The pathway shown in our model agrees with the human colonization history of the different islands in the Galapagos. Our model, in conjunction with the clustering patterns of the individuals (based on genetic distances), suggests that guava introduction history in the Galapagos archipelago was driven by either a single event or a series of introduction events in rapid succession. We thus show that genetic analyses supported by historical sources can be used to track the arrival and spread of invasive species in novel habitats and the potential role of human activities in such processes.