Cellular responses to chemical cues are at the core of a myriad of fundamental biological processes ranging from embryonic development to cancer metastasis. Most of these biological processes are also influenced by mechanical cues such as the stiffness of the extracellular matrix. How a biological function is influenced by a synergy between chemical concentration and extracellular matrix stiffness is largely unknown, however, because no current strategy enables the integration of both types of cues in a single experiment. Here we present a robust microfluidic device that generates a stable, linear and diffusive chemical gradient over a biocompatible hydrogel with a well-defined stiffness gradient. Device fabrication relies on patterned PSA (Pressure Sensitive Adhesive) stacks that can be implemented with minimal cost and lab equipment. This technique is suitable for long-term observation of cell migration and application of traction force microscopy. We validate our device by testing MDCK cell scattering in response to perpendicular gradients of hepatocyte growth factor (HGF) and substrate stiffness.