c. 1400, "subordinate officer, one given the full power of an officer without holding the office," from Anglo-French deputé, noun use of past-participle of Old French députer "appoint, assign" (14c.), from Late Latin deputare "to destine, allot," in classical Latin "to esteem, consider, consider as," literally "to cut off, prune," from de- "away" (see de-) + putare "to think, count, consider," literally "to cut, prune," from PIE root *pau- (2) "to cut, strike, stamp."
Meaning "person appointed or elected to act in the place of another or others" is from 1769.