Evidence of eukaryote-to-eukaryote lateral gene transfer (LGT) has accumulated in recent years, but the selective pressures governing the evolutionary fate of these genes within recipient species remain largely unexplored. Among non-parasitic plants, successful LGT has been reported between different grass species. Here, we use the grass Alloteropsis semialata, a species that possesses multigene LGT fragments that were acquired recently from distantly related grass species, to test the hypothesis that the successful LGT conferred an advantage and were thus rapidly swept into the recipient species. Combining whole-genome and population-level RAD sequencing, we show that the multigene LGT fragments were rapidly integrated in the recipient genome, likely due to positive selection for genes encoding proteins that added novel functions. These fragments also contained physically linked hitchhiking protein-coding genes, and subsequent genomic erosion has generated gene presence-absence polymorphisms that persist in multiple geographic locations, becoming part of the standing genetic variation. Importantly, one of the hitchhiking genes underwent a secondary rapid spread in some populations. This shows that eukaryotic LGT can have a delayed impact, contributing to local adaptation and intraspecific ecological diversification. Therefore, while short-term LGT integration is mediated by positive selection on some of the transferred genes, physically linked hitchhikers can remain functional and augment the standing genetic variation with delayed adaptive consequences.