Two dry surfaces can instantly adhere upon contact with each other through intermolecular forces such as hydrogen bonds, electrostatic interactions and van der Waals interactions1,2. However, such instant adhesion is challenging when wet surfaces such as body tissues are involved, because water separates the molecules of the two surfaces, preventing interactions3,4. Although tissue adhesives have potential advantages over suturing or stapling5,6, existing liquid or hydrogel tissue adhesives suffer from several limitations: weak bonding, low biological compatibility, poor mechanical match with tissues, and slow adhesion formation5-13. Here we propose an alternative tissue adhesive in the form of a dry double-sided tape (DST) made from a combination of a biopolymer (gelatin or chitosan) and crosslinked poly(acrylic acid) grafted with N-hydrosuccinimide ester. The adhesion mechanism of this DST relies on the removal of interfacial water from the tissue surface, resulting in fast temporary crosslinking to the surface. Subsequent covalent crosslinking with amine groups on the tissue surface further improves the adhesion stability and strength of the DST. In vitro mouse, in vivo rat and ex vivo porcine models show that the DST can achieve strong adhesion between diverse wet dynamic tissues and engineering solids within five seconds. The DST may be useful as a tissue adhesive and sealant, and in adhering wearable and implantable devices to wet tissues.