Members, who may serve no more than two four-year terms, are not paid.

State university boards wield enormous power in hiring and firing the president, setting tuition rates, managing finances and approving faculty tenure.

Two members — medical executive W. Heywood Fralin, who helped organize Sullivan’s reinstatement, and lawyer Glynn D. Key — were not eligible for reappointment. Investor Robert D. Hardie was not reappointed to a second term.

McDonnell also filled the remainder of Mark J. Kington’s term after the vice rector resigned from the board last week, and a new board seat was created by the General Assembly.

McDonnell has said he looks for board members who share his goals of reducing college costs, increasing slots for in-state students and making schools more efficient. He has not generally reappointed board members selected by Kaine, but Dragas is an exception.