He replaces Judge Lester Pearce, who resigned April 30 to run for a seat on the board.
Jones is a former vice mayor of Mesa and served nearly nine years on the Mesa City Council.
There are 25 justice courts in Maricopa County that hear a combined caseload of more than 400,000 cases each year. That includes civil lawsuits where the amount in dispute is $10,000 or less, landlord and tenant controversies, small claims cases and civil and criminal traffic offenses, including DUIs.
Justices of the Peace also resolve other types of misdemeanor allegations and handle requests for orders of protection and injunctions against harassment.