Despite the development of hydrogels with high mechanical properties, insufficient adhesion between these materials and biological surfaces significantly limits their use in the biomedical field. By controlling toughening processes, we designed a composite double-network hydrogel with ∼90% water content, which creates a dissipative interface and robustly adheres to soft tissues such as cartilage and meniscus. A double-network matrix composed of covalently cross-linked poly(ethylene glycol) dimethacrylate and ionically cross-linked alginate was reinforced with nanofibrillated cellulose. No tissue surface modification was needed to obtain high adhesion properties of the developed hydrogel. Instead, mechanistic principles were used to control interfacial crack propagation. Comparing to commercial tissue adhesives, the integration of the dissipative polymeric network on the soft tissue surfaces allowed a significant increase in the adhesion strength, such as ∼130 kPa for articular cartilage. Our findings highlight the significant role of controlling hydrogel structure and dissipation processes for toughening the interface. This research provides a promising path to the development of highly adhesive hydrogels for tissues repair.