A tissue adhesive formed by reacting an aminodextran containing primary amine groups with an oxidized dextran containing aldehyde groups is described. The dextran-based polymer tissue adhesive is particularly useful in medical applications where low swell and slow degradation are needed, for example sealing the dura, ophthalmic procedures, tissue repair, antiadhesive applications, drug delivery, and as a plug to seal a fistula or the punctum.