Tough adhesion between wet materials (i.e., synthetic hydrogels and biological tissues) is undergoing intense development, but methods reported so far either require functional groups from the wet materials, involve toxic chemicals, or result in unstable adhesion. Here, we present a method to achieve biocompatible, covalent adhesion, without requiring any functional groups from the wet materials. We use two hydrogels as model adherends that have covalent polymer networks, but have no functional groups for adhesion. We use an aqueous solution of biopolymers and bioconjugate agents as a model adhesive. When the solution is spread at the interface of the hydrogels, the biopolymers diffuse into both hydrogels and cross-link into a covalent network in situ, in topological entanglement with the two polymer networks of the hydrogels. We characterize the chemistry and mechanics of the covalent topological adhesion. In a physiological fluid, the covalent topological adhesion is stable, but a noncovalent topological adhesion separates. Covalent topological adhesion presents immediate opportunities to advance the art of adhesion in diverse and complex environments.