Recently, gas disks have been discovered around main sequence stars well beyond the usual protoplanetary disk lifetimes (i.e., > 10 Myrs), when planets have already formed. These gas disks, mainly composed of CO, carbon, and oxygen seem to be ubiquitous in systems with planetesimal belts (similar to our Kuiper belt), and can last for hundreds of millions of years. Planets orbiting in these gas disks will accrete a large quantity of gas that will transform their primordial atmospheres into new secondary atmospheres with compositions similar to that of the parent gas disk. Here, we quantify how large a secondary atmosphere can be created for a variety of observed gas disks and for a wide range of planet types. We find that gas accretion in this late phase is very significant and an Earths atmospheric mass of gas is readily accreted on terrestrial planets in very tenuous gas disks. In slightly more massive disks, we show that massive CO atmospheres can be accreted, forming planets with up to sub-Neptune-like pressures. Our new results demonstrate that new secondary atmospheres with high metallicities and high C/O ratios will be created in these late gas disks, resetting their primordial compositions inherited from the protoplanetary disk phase, and providing a new birth to planets that lost their atmosphere to photoevaporation or giant impacts. We therefore propose a new paradigm for the formation of atmospheres on low-mass planets, which can be tested with future observations (JWST, ELT, ARIEL). We also show that this late accretion would show a very clear signature in Sub-Neptunes or cold exo-Jupiters. Finally, we find that accretion creates cavities in late gas disks, which could be used as a new planet detection method, for low mass planets a few au to a few tens of au from their host stars.