Bioprinting is a powerful tool for engineering living tissues, however replicating native composition, structure and function remains a major challenge. During morphogenesis, cellular self-organization and matrix development are strongly influenced by the mechanical constraints provided by surrounding tissues, suggesting that such biophysical cues should be integrated into bioprinting strategies to engineer more biomimetic grafts. Here we introduce a novel 4D bioprinting platform that spatially patterns mesenchymal stem/stromal cell (MSC)-derived microtissues into temporally adapting support baths. By modulating the bath`s mechanical properties, we can precisely control the physical constraints applied post-printing, directing both filament geometry and cellular behavior. Support bath stiffness regulated mechano-sensitive gene expression and microtissue phenotype, with softer matrices favoring chondrogenesis and stiffer environments promoting (myo)fibrogenic differentiation. In addition, the physical properties of the support bath modulated microtissue fusion and extracellular matrix organization, with increased collagen fiber alignment in stiffer baths. Leveraging these findings, it was possible to engineer either articular cartilage, meniscus, or ligament grafts with user defined collagen architectures by simply varying the physical properties of the support bath. This platform establishes a foundation for bioprinting structurally anisotropic and phenotypically distinct constructs, thereby enabling the scalable engineering of a range of different musculoskeletal tissues.