Mediterranean annual grasses have invaded California and have replaced vast areas of native grassland. One of these invasive grasses is Brachypodium distachyon, a new model species for the grasses with extensive genomic resources and a nearly completed genome sequence. This study shows that the level of genetic variation in invaded California grasslands is lower compared to the native range in Eurasia. The invaded regions are characterized by highly differentiated populations of B. distachyon isolated by distance, most likely as a result of founder effects and a dearth of outcrossing events. EXP6 and EXP10 encoding alpha-expansins responsible for rapid growth, and AGL11 and AGL13 encoding proteins involved in vegetative phase regulation, appear to be under purifying selection with no evidence for local adaptation. Our data show that B. distachyon has diverged only recently from related Brachypodium species and that tetraploidization might have been as recent as a few thousand years ago. Observed low genetic variation in EXP10 and AGL13 appears to have been present in Eurasia before tetraploidization, potentially as a result of strong selective pressures on advantageous mutations, which are most likely responsible for its fast growth and rapid completion of its life cycle.