"providing safe storage for valuables of any kind," by 1864; see safe (adj.) + deposit (n.).
Entries linking to safe-deposit
safe adj.
c. 1300, sauf, "unscathed, unhurt, uninjured; free from danger or molestation, in safety, secure; saved spiritually, redeemed, not damned;" from Old French sauf "protected, watched-over; assured of salvation," from Latin salvus "uninjured, in good health, safe," which is related to salus "good health," saluber "healthful" (all from PIE *solwos from root *sol- "whole, well-kept"). For the phonological development of safe from sauf, OED compares gage from Old North French gauge.
From late 14c. as "rescued, delivered; protected; left alive, unkilled." The meaning "not exposed to danger" (of places, later of valuables) is attested from late 14c.; in reference to actions, etc., the meaning "free from risk," is recorded by 1580s. The sense of "sure, reliable, not a danger" is from c. 1600. The sense of "conservative, cautious" is from 1823. It has been paired alliteratively with sound (adj.) from c. 1300. In Middle English it also meant "in good health," also "delivered from sin or damnation." Related: Safeness.
deposit n.
1620s, "state of being placed in safe-keeping," from Latin depositum, from deponere (see deposit (v.)). From 1660s as "that which is laid or thrown down." Geological sense is from 1781; financial sense "money lodged in a bank for safety or convenience" is from 1737. Middle English had depost "thing entrusted for safe-keeping" (late 14c.).