We report an experimental study of 1/f noise in liquid-gated graphene transistors. We show that the gate dependence of the noise is well described by a charge-noise model, whereas Hooge's empirical relation fails to describe the data. At low carrier density, the noise can be attributed to fluctuating charges in close proximity to the graphene, while at high carrier density it is consistent with noise due to scattering in the channel. The charge noise power scales inversely with the device area, and bilayer devices exhibit lower noise than single-layer devices. In air, the observed noise is also consistent with the charge-noise model.