Biological tissues, such as tendons or cartilage, possess high strength and toughness with very low plastic deformations. In contrast, current strategies to prepare tough hydrogels commonly utilize energy dissipation mechanisms based on physical bonds that lead to irreversible large plastic deformations, thus limiting their load‐bearing applications. This article reports a strategy to toughen hydrogels using fibrillar connected double networks (fc‐DN), which consist of two distinct but chemically interconnected polymer networks, that is, a polyacrylamide network and an acrylated agarose fibril network. The fc‐DN design allows efficient stress transfer between the two networks and high fibril alignment during deformation, both contributing to high strength and toughness, while the chemical crosslinking ensures low plastic deformations after undergoing high strains. The mechanical properties of the fc‐DN network can be readily tuned to reach an ultimate tensile strength of 8 MPa and a toughness of above 55 MJ m−3, which is 3 and 3.5 times more than that of fibrillar double network hydrogels without chemical connections, respectively. The application potential of the fc‐DN hydrogel is demonstrated as load‐bearing damping material for a jointed robotic lander. The fc‐DN design provides a new toughening mechanism for hydrogels that can be used for soft robotics or bioelectronic applications.