Old English bodian "proclaim, announce; announce beforehand, foretell," from boda "messenger," probably from Proto-Germanic *budon- (source also of Old Saxon gibod, German gebot, Old Norse boð), from PIE root *bheudh- "be aware, make aware."
With good or ill, "give a (good or bad) portent or promise," late 14c. As a shortened form of forebode "presage" (usually something evil), it dates from 1740. Related: Boded; boding.