One of the most promising recent developments in materials science and engineering is the concept of exploiting “architecture” ─ the combination of topology and solid(s) distribution ─ as a means to generate materials with properties that are unattainable by traditional monolithic solids. Lightweight architected materials, such as additively manufactured micro-lattices and random foams, are excellent candidates for a plethora of engineering applications ranging from space structures to battery electrodes and biomedical implants. To date, a wide range of strut- and shell-based architected metamaterials with unique effective properties have been successfully designed and synthesized. Despite their significance, however, a rigorous framework for associating specific mechanical properties of these material systems to key features of their complex microstructure remains an open challenge. We present here a data-driven framework that allows structure-property correlation for both ordered and disordered cellular solids. Representative lattice microstructures are first generated by solid distribution on k-uniform tilings and Laguerre tessellations with large variations of topological characteristics. A set of deterministic and stochastic morphological descriptors is used to perform microstructure quantification for all designs. Finite element simulations, validated by experiments on additively manufactured specimens, are then performed to predict the macroscopic elastic modulus for different sets of material designs. The numerical data are introduced in machine learning algorithms to develop a surrogate model with the ability to (a) predict macroscopic properties and (b) correlate them to the key morphological descriptors. Results will be presented for 2D materials, including identification of the microstructural descriptors with the largest effect on their effective stiffness. We will further show how this framework can be used to design materials with specific mechanical properties that are also imperfection-insensitive.