1560s, devest (modern spelling is c. 1600), "strip of possessions," from Middle French devester "strip of possessions" (Old French desvestir), from des- "away" (see dis-) + vestir "to clothe," from Latin vestire "to clothe," from PIE *wes- (2) "to clothe," extended form of root *eu- "to dress."
The etymological sense of "strip of clothes, arms, or equippage" is from 1580s. Meaning "strip by some definite or legal process" is from 1570s. Economic sense "sell off (a subsidiary company, later an investment) is by 1961. Related: Divested; divesting.