Old English storm, from Proto-Germanic *sturmaz (cf. Old Norse stormr, Old Saxon, Middle Low German, Middle Dutch, Dutch storm, Old High German and German sturm). Old French estour "onset, tumult," Italian stormo are Germanic loan-words. Figurative (non-meteorological) sense was in late Old English.
Storm-door first recorded 1878; storm-water is from 1879; storm-window is attested from 1824. Storm surge attested from 1929.