If, in a referendum held as provided in § 22.1-42, it shall be determined that the members of the county school board shall be appointed by the governing body of the county, such governing body shall, by majority vote, thereafter appoint all members of the school board and the tie breaker, if any. Members of the school board and the tie breaker in office at the time of the referendum shall complete their terms and their successors shall be appointed by the governing body. The governing body shall determine whether the office of the tie breaker shall continue after the expiration of the term of the incumbent. Appointments of school board members and tie breakers, if any, shall be made at public meetings. The terms of office of the members of the county school board shall continue to be four years. Vacancies in the office of members of the county school board occurring other than by expiration of term shall be filled by appointment by the governing body for the unexpired terms. The term of office of the tie breaker, if any, shall continue to be four years. Any appointment to fill a vacancy in the office of tie breaker, if any, whether or not by expiration of term, shall be for a four-year term. The school board shall consist of the same number of members from each magisterial or election district as is provided in § 22.1-36. The governing body of the county may appoint no more than two additional members from the county at large.