Organoids are powerful models of tissue physiology, yet their applications remain limited due to their relatively simple morphology and high organoid-to-organoid structural variability. To address these limitations we developed a soft, composite yield-stress extracellular matrix that supports optimal organoid morphogenesis following freeform 3D bioprinting of cell slurries at tissue-like densities. The material is designed with two temperature regimes: at 4 °C it exhibits reversible yield-stress behavior to support long printing times without compromising cell viability. When transferred to cell culture at 37 °C, the material cross-links and exhibits similar viscoelasticity and plasticity to basement membrane extracts such as Matrigel. We first characterize the rheological properties of MAGIC matrices that optimize organoid morphogenesis, including low stiffness and high stress relaxation. Next, we combine this material with a custom piezoelectric printhead that allows more reproducible and robust self-organization from uniform and spatially organized tissue "seeds." We apply MAGIC matrix bioprinting for high-throughput generation of intestinal, mammary, vascular, salivary gland, and brain organoid arrays that are structurally similar to those grown in pure Matrigel, but exhibit dramatically improved homogeneity in organoid size, shape, maturation time, and efficiency of morphogenesis. The flexibility of this method and material enabled fabrication of fully 3D microphysiological systems, including perfusable organoid tubes that experience cyclic 3D strain in response to pressurization. Furthermore, the reproducibility of organoid structure increased the statistical power of a drug response assay by up to 8 orders-of-magnitude for a given number of comparisons. Combined, these advances lay the foundation for the efficient fabrication of complex tissue morphologies by canalizing their self-organization in both space and time.