Disclosed herein is a fibrous tissue sealant in the form of an anhydrous fibrous sheet comprising a first component which is a fibrous polymer containing electrophilic or nucleophilic groups and a second component capable of crosslinking the first component when the sheet is exposed to an aqueous medium, thereby forming a crosslinked hydrogel that is adhesive to biological tissue. The fibrous tissue sealant may be useful as a general tissue adhesive for medical and veterinary applications such as wound closure, supplementing or replacing sutures or staples in internal surgical procedures, tissue repair, and to prevent post-surgical adhesions. The fibrous tissue sealant may be particularly suitable for use as a hemostatic sealant to stanch bleeding from surgical or traumatic wounds.