The mechanical properties of cells are largely determined by the cytoskeleton, which is a complex network of interconnected biopolymers consisting of actin filaments, microtubules, and intermediate filaments. While disruption of the actin filament and microtubule networks is known to decrease and increase cell-generated forces, respectively, the effect of intermediate filaments on cellular forces is not well understood. Using a combination of theoretical modeling and experiments, we show that disruption of vimentin intermediate filaments can either increase or decrease cell-generated forces, depending on microenvironment stiffness, reconciling seemingly opposite results in the literature. On the one hand, vimentin is involved in the transmission of actomyosin-based tensile forces to the matrix and therefore enhances traction forces. On the other hand, vimentin reinforces microtubules and their stability under compression, thus promoting the role of microtubules in suppressing cellular traction forces. We show that the competition between these two opposing effects of vimentin is regulated by the microenvironment stiffness. For low matrix stiffness, the force-transmitting role of vimentin dominates over their microtubule-reinforcing role and therefore vimentin increases traction forces. At high matrix stiffness, vimentin decreases traction forces as the microtubule-reinforcing role of vimentin becomes more important with increasing matrix stiffness. Our theory reconciles seemingly disparate experimental observations on the role of vimentin in active cellular forces and provides a unified description of stiffness-dependent chemo-mechanical regulation of cell contractility by vimentin.