c. 1300, charmen, "to recite or cast a magic spell," from Old French charmer (13c.) "to enchant, to fill (someone) with desire (for something); to protect, cure, treat; to maltreat, harm," from Late Latin carminare, from Latin carmen "song, verse, enchantment, religious formula" (see charm (n.)).
In Old French used alike of magical and non-magical activity. In English, "to win over by treating pleasingly, delight" from mid-15c.; the weaker sense of "be highly pleasing" is by early 18c. Charmed as a conventional reply to a greeting or meeting (short for I am charmed) is attested by 1825.