Between 1973 and 2003 mean morphological features of the cactus finch, Geospiza scandens, and the medium ground finch, G. fortis, populations on the Galápagos island of Daphne Major were subject to fluctuating directional selection. An increase in bluntness or robustness in the beak of G. scandens after 1990 can only partly be explained by selection. We use 16 microsatellite loci to test predictions of the previously proposed hypothesis that introgressive hybridization contributed to the trend, resulting in genes flowing predominantly from G. fortis to G. scandens. To identify F1 hybrids and backcrosses we use pedigrees where known, supplemented by the results of assignment tests based on 14 autosomal loci when parents were not known. We analyze changes in morphology and allelic composition in the two populations over a period of 15-20 years. With samples that included F1 hybrids and backcrosses, the G. scandens population became more similar to the G. fortis population both genetically and morphologically. Gene flow between species was estimated to be three times greater from G. fortis to G. scandens than in the opposite direction, resulting in a 20% reduction in the genetic difference between the species. Nevertheless, removing identified F1 hybrids and backcrosses from the total sample and reanalyzing the traits did not eliminate the convergence. The two species also converged in beak shape by 22.2% and in body size by 45.5%. A combination of introgressive hybridization and selection jointly provide the best explanation of convergence in morphology and genetic constitution under the changed ecological conditions following a major El Niño event in 1983. The study illustrates how species without postmating barriers to gene exchange can alternate between convergence and divergence when environmental conditions oscillate.