According to the University of Nebraska-Lincoln Extension, seeding after the use of glyphosate can safely be done on the day of application. This is because the chemical is systemic in nature, affecting only the already-growing plants and not the ones that haven't yet emerged. Roundup, with the active ingredient glyphosate, has no activity in the soil and will not harm seeds.
There are certain formulations of Roundup that come with pre-emergent herbicides intended for the control of weeds all season in hard-to-reach places such as sidewalks. Pre-emergent herbicides control weeds by retarding the germination of weed seeds, but the chemicals will also affect germination of grass seeds. Areas that have been treated with Roundup containing pre-emergent herbicides cannot be seeded immediately after application.
When Roundup is applied on hard-to-control grasses and weeds, the treated areas need to be raked or aerated so the chemical can reach all plant parts. Tough-to-control grasses or weeds are those that have rhizomes, or stolons; examples include bermudagrass, zoysiagrass, tall fescues, quackgrass and Kentucky bluegrass. When applying Roundup to these and others stolonous plants, allow time for repeat application prior to reseeding.
Often the target areas have to be seeded immediately following Roundup application, because a delay that forces planting to be done too late in the season is likely to impede healthy germination of newly planted seeds. In cases where there's no time to allow for repeat application of the herbicide, it's recommended to leave the weeds as they are and then treat with either glyphosate or other herbicides the next year, when there's enough time for repeat applications if required.