During angiogenesis, cytoskeletal dynamics that mediate endothelial cell branching morphogenesis during vascular guidance are thought to be regulated by physical attributes of the extracellular matrix (ECM) in a process termed mechanosensing. Here, we tested the involvement of microtubules in linking mechanosensing to endothelial cell branching morphogenesis. We used a recently developed microtubule plus end-tracking program to show that specific parameters of microtubule assembly dynamics, growth speed and growth persistence, are globally and regionally modified by, and contribute to, ECM mechanosensing. We demonstrated that engagement of compliant two-dimensional or three-dimensional ECMs induces local differences in microtubule growth speed that require myosin II contractility. Finally, we found that microtubule growth persistence is modulated by myosin II-mediated compliance mechanosensing when cells are cultured on two-dimensional ECMs, whereas three-dimensional ECM engagement makes microtubule growth persistence insensitive to changes in ECM compliance. Thus, compliance and dimensionality ECM mechanosensing pathways independently regulate specific and distinct microtubule dynamics parameters in endothelial cells to guide branching morphogenesis in physically complex ECMs.