Organoids are powerful models of tissue physiology, yet their applications remain limited due to a lack of complex tissue morphology and high organoid-to-organoid structural variability. To address these limitations we developed a soft, composite yield-stress extracellular matrix that supports freeform 3D bioprinting of cell slurries at tissue-like densities. Combined with a custom piezoelectric printhead, this platform allows more reproducible and complex morphogenesis from uniform and spatially organized organoid “seeds.” At 4 °C the material 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 use this setup for high-throughput generation of intestinal and salivary gland organoid arrays that are morphologically indistinguishable from those grown in pure Matrigel, but exhibit dramatically improved homogeneity in organoid size, shape, maturation time, and budding efficiency. The reproducibility of organoid structure afforded by this approach increases the sensitivity of assays by orders of magnitude, requiring less input material and reducing analysis times. The flexibility of this approach additionally enabled the fabrication of perfusable intestinal organoid tubes. Combined, these advances lay the foundation for the efficient design of complex tissue morphologies in both space and time.