1590s, "answerable" (to another, for something), from obsolete French responsible (13c., Modern French responsable, as if from Latin *responsabilis), from Latin respons-, past-participle stem of respondere "respond, answer to, promise in return," from re- "back" (see re-) + spondere "to pledge" (see sponsor (n.)).
Meaning "accountable for one's actions" is attested from 1640s; that of "reliable, trustworthy" is from 1690s. It retains the sense of "obligation" in the Latin root word. Related: Responsibly.