Piezoelectric coefficients are constrained by the intrinsic crystal structure of the constituent material. Here we describe design and manufacturing routes to previously inaccessible classes of piezoelectric materials that have arbitrary piezoelectric coefficient tensors. Our scheme is based on the manipulation of electric displacement maps from families of structural cell patterns. We implement our designs by additively manufacturing free-form, perovskite-based piezoelectric nanocomposites with complex three-dimensional architectures. The resulting voltage response of the activated piezoelectric metamaterials at a given mode can be selectively suppressed, reversed or enhanced with applied stress. Additionally, these electromechanical metamaterials achieve high specific piezoelectric constants and tailorable flexibility using only a fraction of their parent materials. This strategy may be applied to create the next generation of intelligent infrastructure, able to perform a variety of structural and functional tasks, including simultaneous impact absorption and monitoring, three-dimensional pressure mapping and directionality detection.