eligible (adj.)

c. 1300, eleccioun, "act of choosing" someone to occupy a position, elevation to office" (whether by one person or a body of electors); also "the holding of a vote by a body of electors by established procedure; the time and place of such a vote," from Anglo-French eleccioun, Old French elecion "choice, election, selection" (12c.), from Latin electionem (nominative electio) "a choice, selection," noun of action from past-participle stem of eligere "pick out, select," from ex "out" (see ex-) + -ligere, combining form of legere "to choose," from PIE root *leg- (1) "to collect, gather."

In Middle English also "act of choosing" generally, "choice, free choice" (c. 1400). The theological sense of "God's choice of someone" for eternal life is from late 14c. Meaning "act of choosing, choice" is from c. 1400.

1640s, "worthiness to be chosen," from eligible + -ity. From 1715 as "legal qualification to be chosen."

1763, from in- (1) "not, opposite of" + eligible. Perhaps modeled on French inéligible. Related: Ineligibility.