Elastomeric, robust, and biocompatible hydrogels are rare, while the need for these types of biomaterials in biomedical-related uses remains high. Here, a new family of genetically engineered silk-elastin copolymers (SELPs) with encoded enzymatic crosslinking sites is developed for a new generation of stimuli-responsive yet robust hydrogels. Input into the designs is guided by simulation, and realized via genetic engineering strategies. The avoidance of gamma irradiation or chemical crosslinking during gel fabrication, in lieu of an enzymatic process, expands the versatility of these new gels for the incorporation of labile proteins and cells. In the present study, the new SELP hydrogels offers sequence dependent, reversible stimuli-responsive features. Their stiffness covers almost the full range of the elasticity of soft tissues. Further, physical modification of the silk domains provided a secondary control point to fine-tune mechanical stiffness while preserving stimuli-responsive features, with implications for a variety of biomedical materials and device needs.