We demonstrate humidity sensing using a change of the electrical resistance of single-layer chemical vapor deposited (CVD) graphene that is placed on top of a SiO2 layer on a Si wafer. To investigate the selectivity of the sensor towards the most common constituents in air, its signal response was characterized individually for water vapor (H2O), nitrogen (N2), oxygen (O2), and argon (Ar). In order to assess the humidity sensing effect for a range from 1% relative humidity (RH) to 96% RH, the devices were characterized both in a vacuum chamber and in a humidity chamber at atmospheric pressure. The measured response and recovery times of the graphene humidity sensors are on the order of several hundred milliseconds. Density functional theory simulations are employed to further investigate the sensitivity of the graphene devices towards water vapor. The interaction between the electrostatic dipole moment of the water and the impurity bands in the SiO2 substrate leads to electrostatic doping of the graphene layer. The proposed graphene sensor provides rapid response direct electrical readout and is compatible with back end of the line (BEOL) integration on top of CMOS-based integrated circuits.