Extracellular matrix (ECM) structure, composition, and stiffness have profound effects on tissue development and pathologies such as cardiovascular disease and cancer. Accordingly, a variety of synthetic hydrogel systems have been designed to study the impact of ECM composition, density, mechanics, and topography on cell and tissue phenotype. However, these synthetic systems fail to accurately recapitulate the biological properties and structure of the native tissue ECM. Natural three dimensional (3D) ECM hydrogels, such as collagen or hyaluronic acid, feature many of the chemical and physical properties of tissue, yet, these systems have limitations including the inability to independently control biophysical properties such as stiffness and pore size. Here, we present a 3D tension bioreactor system that permits precise mechanical tuning of collagen hydrogel stiffness, while maintaining consistent composition and pore size. We achieve this by mechanically loading collagen hydrogels covalently-conjugated to a polydimethylsiloxane (PDMS) membrane to induce hydrogel stiffening. We validated the biological application of this system with oncogenically transformed mammary epithelial cell organoids embedded in a 3D collagen I hydrogel, either uniformly stiffened or calibrated to create a gradient of ECM stiffening, to visually demonstrate the impact of ECM stiffening on transformation and tumor cell invasion. As such, this bioreactor presents the first tunable 3D natural hydrogel system that is capable of independently assessing the role of ECM stiffness on tissue phenotype.