1725, from un- (1) "not" + past participle of need (v.).
Entries linking to unneeded
un- 1
prefix of negation, Old English un-, from Proto-Germanic *un- (source also of Old Saxon, Old Frisian, Old High German, German un-, Gothic un-, Dutch on-), from PIE *n- (source of Sanskrit a-, an- "not," Greek a-, an-, Old Irish an-, Latin in-), combining form of PIE root *ne- "not." Often euphemistic (such as untruth for "lie").
The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It underwent a mass extinction in early Middle English, but emerged with renewed vigor 16c. to form compounds with native and imported words. It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.
It also makes words from phrases (such as uncalled-for, c. 1600; undreamed-of, 1630s; uncome-at-able, 1690s; unputdownable, 1947, of a book; un-in-one-breath-utterable, Ben Jonson; etc., but the habit is not restricted to un-; such as put-up-able-with, 1812). As a prefix in telegramese to replace not and save the cost of a word, it is attested by 1936.
need v.
Old English neodian "be necessary, be required (for some purpose)," intransitive; also transitive, "require, have need of," from the same root as need (n.). Meaning "to be under obligation (to do something)," especially in negative or interrogative sentences implying obligation or necessity, is from late 14c. Related: Needed; needing. The adjectival phrase need-to-know is attested from 1952. Dismissive phrase who needs it?, popular from c. 1960, is a translated Yiddishism.
Need, especially in negative and interrogative sentences implying obligation or necessity, is often used, in the present, before an infinitive, usually without to, need being then invariable (without the personal terminations of the second and third persons singular): as, he or they need not go; need he do it? [Century Dictionary]