The amount of reclaimed asphalt pavement (RAP) after roadway milling procedures is high, and it cannot be completely recycled within asphalt. Therefore, to save landfill space, the recycling of uncontaminated RAP aggregates within concrete was deeply studied. The combination of two blended cements and the addition of 30% RAP to replace natural aggregates allowed an appropriate control of the early strength and stiffness development of the RAP concrete. The strength values remained in the range of 36–43 MPa up to 60 d, and the modulus of elasticity was between 27500 MPa and 28500 MPa. The control of these two parameters within the early hydration stage and the RAP addition was essential to avoid the formation of microcracks and to obtain waterproof concrete. The fine RAP component allowed adequate densification and the production of watertight recycled concrete. The leaching tests indicated a very low environmental risk with respect to the pollutant release.