Lightweight aggregates are extensively used in construction and other industrial applications due to their technological characteristics. The extraction of natural aggregates results in serious environmental effects. Thus, within the circular economy concept, the valorization of waste through the optimization of materials and product design is encouraged. In this work, glass lightweight aggregates were prepared from mixtures of white glass cullet and carbonate wastes from mining (wastes originating from the extraction, manufacture and marketing of magnesite and its derivatives) and the food industry (eggshell and mussel shell). The effects of different processing parameters, such as the particle size of the base glass, percentage of the blowing additive, shaping method, heating rate, temperature and processing time, were evaluated. The results indicate that the mineralogical composition of the blowing agent and the particle size of the base glass are the two processing parameters with the greatest impact on expansion efficiency. Thus, glass artificial aggregates were obtained with characteristics similar to those of commercial products (density values ranged between 0.3 and 0.8 g/cm3 and mechanical strength between 0.7 and 1.5 MPa) from thermal shock expansion treatments in the temperature range 800–900 °C and with dwell times no longer than 15 min.