A tire air pressure monitoring system is provided that comprises a transmitting device, a receiving device, and a tire identification number registration device. The transmitting device is mounted on a wheel of a vehicle, and configured and arranged to wirelessly transmit a signal indicative of at least tire air pressure information of a tire coupled to the wheel and a tire identification number assigned to the wheel. The receiving device is mounted on the vehicle, and configured and arranged to receive the signal transmitted from the transmitting device. The tire identification number registration device is configured to estimate a position of the wheel with respect to the vehicle based on correlation information corresponding to an extent of a correlation between strength of the signal and a tire rotational angle of the wheel, and to register the tire identification number with the position of the wheel.