Where does the use of the term "Vice" come from when refering to a person who previously held a position.?

For example ... "I'd like to backfill the Financial Analyst - vice Smith position" or "I'd like to recruit for one of the vacant positions in my office; Secretary - vice Jones"

I work with the Federal Government, and it seems like everyone understands that "vice" is the last person to hold that position, but I don't see that in the definition of "vice". Just wondering how/why that term came about.