"having power to relieve pain," 1540s, from Medieval Latin anodynus "pain-removing, allaying pain," from Latin anodynus "painless," from Greek anodynos "free from pain," from an- "without" (see an- (1)) + odyne "pain, torment" (of the body or mind), a word of uncertain origin, evidently Indo-European, but none of the proposed etymologies satisfies Beekes. Some suggest it is a suffixed form of PIE root *ed- "to eat" (compare Lithuanian ėdžioti "to devour, bite," ėdžiotis "to suffer pain").
As a noun, "substance which alleviates pain," 1540s; in old slang, frequently a euphemism for "death" (as the final relief from the mental pain or distress of life) as in anodyne necklace "hangman's noose." Related: Anodynous.