Connecting unmanned aerial vehicles (UAVs) by using cellular networks can significantly expand the civil applications of UAVs, due to much a larger connectivity range and low cost. However, the low-altitude air-to-ground (ATG) channels are different from the traditional terrestrial mobile access channels, and hence need to be characterized specifically. In this paper, a measurement campaign and modeling of the aerial access channels between a UAV and base station (BS) in the typical urban macro-cell (UMa) and rural macro-cell (RMa) scenarios are presented. The channels were sounded at 2.412 GHz and 919 MHz with the horizontal ranges of 420 meters and 10 kilometers, respectively, in the two scenarios. The transmitter equipped with two omnidirectional antennas was fixed on a fourrotor UAV which flew horizontally at various altitudes from 25 to 150 meters. The receiver was installed on the top of five-storey buildings to emulate a BS. The path loss (PL) was measured and the statistical models have been proposed which are based on the corresponding 3GPP territorial channel models but adjusted by adding correction factors (CFs). The CF is relevant to the UAV height in the UMa scenario. For the RMa scenario there is a breaking point with respect to the horizontal distance and hence a segmented function for the CF is proposed. The new PL models can help to establish the ATG channel models and support the design of air-borne access technologies for the LTE networks.