The commissioners shall serve five-year terms, with each term beginning July first and ending on June thirtieth; except, that of the commissioners first appointed, one shall be appointed for a term of two years, two shall be appointed for a term of three years, two shall be appointed for a term of four years, and two shall be appointed for a term of five years. Each commissioner appointed thereafter shall be appointed for a term ending five years from the date of expiration of the term for which his predecessor was appointed; except, that a person appointed to fill a vacancy prior to the expiration of such a term shall be appointed for the remainder of the term. No commissioner appointed pursuant to sections 348.005 to 348.180 by the governor shall serve more than two consecutive full terms. Each commissioner shall hold office for the term of his appointment and until his successor shall have been appointed and qualified.