Mechanical interactions between cells and their surrounding extracellular matrix (ECM) guide many fundamental cell behaviors. Native connective tissue consists of highly organized, 3D networks of ECM fibers with complex, nonlinear mechanical properties. The most abundant stromal matrix component is fibrillar type I collagen, which often possesses a wavy, crimped morphology that confers strain- and load-dependent nonlinear mechanical behavior. Here, we established a new and simple method for engineering electrospun fibrous matrices composed of dextran vinyl sulfone (DexVS) with controllable crimped structure. A hydrophilic peptide was functionalized to DexVS matrices to trigger swelling of individual hydrogel fibers, resulting in crimped microstructure due to the fixed anchorage of fibers. Mechanical characterization of these matrices under tension confirmed orthogonal control over nonlinear stress–strain responses and matrix stiffness. We next examined ECM mechanosensing of individual endothelial cells (ECs) and found that fiber crimp promoted physical matrix remodeling alongside decreases in cell spreading, focal adhesion area, and nuclear localization of Yes-associated protein (YAP). These changes corresponded to an increase in migration speed, along with evidence for long-range interactions between neighboring cells in crimped matrices. Interestingly, when ECs were seeded at high density in crimped matrices, capillary-like networks rapidly assembled and contained tube-like cellular structures wrapped around bundles of synthetic matrix fibers due to increased physical reorganization of matrix fibers. Our work provides an additional level of mechanical and architectural tunability to synthetic fibrous matrices and implicates a critical role for mechanical nonlinearity in EC mechanosensing and network formation.