late 14c., "to clothe in the official robes of an office," from Latin investire "to clothe in, cover, surround," from in "in, into" (from PIE root *en "in") + vestire "to dress, clothe," from PIE *wes- (2) "to clothe," extended form of root *eu- "to dress."
The meaning "use money to produce profit" is attested from 1610s in connection with the East Indies trade, and it is probably a borrowing of a special use of Italian investire (13c., from the same Latin root) via the notion of giving one's capital a new form. The figurative sense of "to clothe (with attributes)" is from c. 1600. The military meaning "to besiege, surround with hostile intent" also is from c. 1600. Related: Invested; investing.