This work aims to develop a method to recover aggregates from existing concrete in the framework of evaluating the ASR (Alkali–Silica Reaction) reactivity of these recovered aggregates. To achieve its purpose, the method should guarantee recovery of the maximum amount of all sizes of aggregates and should dissolve the hydrated cement as completely as possible, without altering the composition of the aggregate. A three-step methodology is proposed: rough crushing of the concrete, separation of cement paste from aggregates through a thermal treatment, and dissolution of the remaining attached mortar by chemical attack. This method was tested on concretes cast with known amounts of aggregates. The recovered aggregates were comparable to natural aggregates regarding their particle size distribution. An efficiency of 90–92% was obtained on quartzite and siliceous limestone, with very high recovery rates for particles larger than 1 mm.