1620s, of decrees, etc., "that cannot be overturned or undone," from assimilated form of in- (1) "not, opposite of" + reversible. Of physical things, "that cannot be turned the other way," from 1821. Related: Irreversibly.
word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
"capable of being reversed" in any sense of that word, 1640s, from reverse (v.) + -ible. As a noun, "garment of a textile fabric having two faces, usually unlike, either of which may be exposed," by 1863. Related: Reversable (1580s).
<a href="https://www.etymonline.com/word/irreversible">Etymology of irreversible by etymonline</a>
Harper, D. (n.d.). Etymology of irreversible. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/irreversible