c. 1500, of persons, "given to extravagant expenditure, lavish, wasteful," a back-formation from prodigality, or else from French prodigal and directly from Late Latin prodigalis, from Latin prodigus "wasteful," from prodigere "drive away, waste," from pro "forth" (from PIE root *per- (1) "forward") + agere "to set in motion, drive; to do, perform" (from PIE root *ag- "to drive, draw out or forth, move").
Most often in prodigal son (Vulgate Latin filius prodigus) from the parable told in Luke xv.11-32. The meaning "very liberal, lavishly bountiful" is by 1590s. As a noun, "prodigal person, one who expends money lavishly and without necessity," 1590s, from the adjective (the Latin adjective also was used as a noun). Related: Prodigially.