We report on the design of a modular, high-temperature thermochemical energy storage system based on endothermic-exothermic reversible gas-solid reactions for application in concentrated solar power and industrial thermal processes. It consists of an array of tubular reactors, each containing an annular packed bed subjected to radial flow, and integrated in series with a thermocline-based sensible thermal energy storage. The calcination-carbonation of limestone, CaCO3 ↔ CaO + CO2, is selected as the reversible thermochemical reaction for the experimental demonstration. Synthetized 4.2 mm-mean size agglomerates and 2 mm-mean size granules of CaO with 42 %wt sintering-inhibitor MgO support attained reaction extents of up to 84.0% for agglomerates and 31.9% for granules, and good cycling stability in pressure-swing and temperature-swing thermogravimetric runs. A lab-scale reactor prototype is fabricated and tested with both formulations for 80 consecutive carbonation-calcination cycles at ambient pressure using a temperature-swing mode between 830°C and 930°C. The reactor exhibited stable cyclic operation and low pressure drop, and yielded specific gravimetric and volumetric heat storage capacities of 866 kJ/kg and 322 MJ/m3 for agglomerates, respectively, and 450 kJ/kg and 134 MJ/m3 for granules, respectively.