mid-13c., babeln "to prattle, utter words indistinctly, talk like a baby," akin to other Western European words for stammering and prattling (Swedish babbla, Old French babillier, etc.) attested from the same era (some of which probably were borrowed from others), all probably ultimately imitative of baby-talk (compare Latin babulus "babbler," Greek barbaros "non-Greek-speaking"). "No direct connexion with Babel can be traced; though association with that may have affected the senses" [OED]. Meaning "to talk excessively" is attested from c. 1500. Related: Babbled; babbler; babbling.
c. 1500, "idle talk," from babble (v.). In 16c., commonly in reduplicated form bibble-babble (1530s). Meaning "inarticulate speech" is from 1660s. Other nouns meaning "idle talk" included babblery (1530s), babblement (1640s).