Cell migration toward stiffer or softer environments (durotaxis) underlies processes from development to cancer metastasis, yet the underlying mechanism and its universality remain unclear. To resolve this, we investigated how traction forces and directional persistence dictate cell migration along stiffness gradients. We utilized tunable PEG hydrogels with stiffness gradients of 1-16 kPa and perturbed contractility (blebbistatin, oligomycin), and adhesion (vinculin mutants), in cancer cells exhibiting opposing durotactic biases. We found that cells exerting high traction forces migrate persistently towards stiffer regions (positive durotaxis), whereas those with reduced traction lose persistence and shift towards softer regions (negative durotaxis). We developed a computational model linking stiffness-dependent traction from a motor-clutch framework to F-actin stability-driven persistence, capturing both behaviors with one parameter set. The model predicts, and experiments confirm, that tuning myosin activity or adhesion reinforcement can switch durotaxis states. These findings establish a unified mechanism where traction-regulated persistence governs durotaxis bias across cell types. This insight advances design of biomaterials for directed cell migration and suggests therapeutic strategies to control cell trafficking in tissue repair and cancer.