We present waveguide-integrated graphene devices for photonic gas sensing. In a gas environment, graphene's conductivity is changed by adsorbed gas molecules which serve as charge-carrier donors or acceptors. To accurately probe gas-induced variations in the graphene's conductivity, we optimize the graphene's Fermi level and spectral region. Then, we propose graphene-on-silicon and ... [Show full abstract] graphene-on-germanium suspended membrane slot waveguides in which propagating light in the waveguide has a strong interaction with the top graphene layer. The gas concentration can be calculated by measuring the spectrum of the optical reflection from the waveguide Bragg grating. The maximum sensitivity of the waveguide-integrated gas sensor can reach one part per million for sensing gaseous nitrogen dioxide. Its sensitivity is about 20 times higher than that of the graphene-covered microfiber sensor and is comparable with that of a graphene plasmonic sensor. The fabrication of the proposed graphene device is CMOS compatible. Our results pave a way for chip-integrated sensitive photonic gas sensors.