1620s, "place in the hands of another as a pledge for a contract," from Latin depositus, past participle of deponere "lay aside, put down, deposit," also used of births and bets, from de "away" (see de-) + ponere "to put, place" (past participle positus; see position (n.)). From 1650s as "lay away for safe-keeping;" from 1749 as "lay down, place, put." Related: Deposited; depositing.
adjective and noun suffix, "having to do with, characterized by, tending to, place for," from Middle English -orie, from Old North French -ory, -orie (Old French -oir, -oire), from Latin -orius, -oria, -orium.
Latin adjectives in -orius, according to "An Etymological Dictionary of the French Language," tended to "indicate a quality proper to the action accomplished by the agent; as oratorius from orator; laudatorius from laudator. The neuter of these adjectives was early employed as a substantive, and usually denoted the place of residence of the agent or the instrument that he uses; as praetorium from praetor; dormitorium from dormitor; auditorium, dolatorium.
"These newer words, already frequent under the Empire, became exceedingly numerous at a later time, especially in ecclesiastical and scholastic Latin; as purgatorium, refectorium, laboratorium, observatorium, &c." [transl. G.W. Kitchin, Oxford, 1878]
<a href="https://www.etymonline.com/word/depository">Etymology of depository by etymonline</a>
Harper, D. (n.d.). Etymology of depository. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/depository