In a classic example of the invasion of a species by a selfish genetic element, the P-element was horizontally transferred from a distantly related species into Drosophila melanogaster, where it caused a syndrome of abnormal phenotypes, including sterility, called “hybrid dysgenesis”. The P-element spread globally in the course of a few decades in D. melanogaster, while its sister species, including D. simulans, remained P-element free. Here, we find hybrid dysgenesis also occurs between D. simulans strains collected in different years; a survey of 154 strains shows that over one-third of them induce hybrid dysgenesis. Using genomic and transcriptomic data, we show that this dysgenesis-inducing phenotype is associated with the presence of the P-element, which has recently invaded D. simulans. We survey 573 D. simulans strains collected over the past 30 years for the presence of the P-element, and find that the D. simulans invasion of the P-element occurred rapidly, with infected strains across three continents being rare in 2004 and common by 2014. Importantly, strains collected from the latter phase of this invasion have adapted to ameliorate the effects of the P-element, as evidenced by their resistance to the hybrid dysgenesis phenotype. This work demonstrates that selfish elements can cause rapid global change in the genomes of their host species, even faster than previously thought.