"to put off till another day, defer to a future time," 1580s, a back formation from procrastination or else from Latin procrastinatus, past participle of procrastinare "to put off till tomorrow; defer, delay." Intransitive sense of "be dilatory" is by 1630s. Related: Procrastinated; procrastinating. The earlier verb was procrastine (1540s), from French procrastiner.
Do not put off till tomorrow what can be put off till day-after-tomorrow just as well. ["Mark Twain," "Advice to Young People," 1882]