Catalyzes the formation of 1,8-cineole from geranyl diphosphate. The enzyme also produces significant amounts of (+)- and (-)-alpha-pinene, (+)- and (-)-beta-pinene, myrcene and (+)-sabinene. (2E)-geranyl diphosphate + H2O = 1,8-cineole + diphosphate Binds 3 Mg(2+) ions per subunit. Monomer. The Asp-Asp-Xaa-Xaa-Asp/Glu (DDXXD/E) motif is important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family.