Recycled aggregate concrete has great significance from the environmental protection perspective. However, the current research findings on its hygrothermal properties are sparse. In this study, the apparent density, thermal conductivity, mass moisture content, water vapor permeability coefficient, water absorption coefficient, and liquid water diffusion coefficient of recycled aggregate concrete were determined by experimental methods. The effect of temperature and humidity on thermal conductivity was also studied. Furthermore, the fitting relations of the thermal conductivity of recycled aggregate concrete with the two variables of temperature and relative humidity were presented. The isothermal moisture absorption curve and the fitting relationship of water vapor permeability coefficient with relative humidity were also developed. The results indicate that the thermal conductivity of the eight recycled concrete specimens in the dry state at 25°C ranges from 0.994 to 1.242 W/(m·K). The thermal conductivity increases with the increase in temperature. When the temperature rises from 25°C to 35°C, the thermal conductivity of recycled aggregate concrete increases by 3.8%–13.5%. With the increase of relative humidity, the thermal conductivity of recycled aggregate concrete shows an increasing trend, followed by a steady state, and finally the increasing trend, showing a cubic function relationship between them. When the relative humidity increases from 0% to 95%, the thermal conductivity increases by about 20%. The mass moisture content and the water vapor permeability coefficient increase with relative humidity. The results of this study can provide basic information for the study on the heat and moisture transfer of recycled aggregate concrete, and enhance the database of hygrothermal properties of building materials.