1580s, "pertaining to or constituting a lengthy heroic poem," via Middle French épique or directly from Latin epicus, from Greek epikos, from epos "a word; a tale, story; promise, prophecy, proverb; poetry in heroic verse," from PIE root *wekw- "to speak."
Extended sense of "grand, heroic" first recorded in English 1731. From 1706 as a noun in reference to an epic poem, "A long narrative told on a grand scale of time and place, featuring a larger-than-life protagonist and heroic actions" [Miller Williams, "Patterns of Poetry"]. Earlier as "an epic poet" (1630s).