Within thirty days after the creation of a new school district pursuant to sections 79-413 to 79-419, the State Committee for the Reorganization of School Districts shall appoint from among the legal voters of the new school district created the number of members necessary to constitute a school board of the class in which the new school district has been classified. Members of the first board shall be appointed so that their terms will expire in accord with provisions of law governing school districts of the class involved. The board so appointed shall organize at once in the manner prescribed by law. A reorganized school district shall be formed, organized, and have a governing board not later than June 1 following the last legal action, as prescribed in section 79-413, necessary to effect the changes in boundaries as set forth in the petition, although the physical reorganization of such reorganized school district may not take effect until the commencement of the following school year. At the next election following the establishment of the new school district and at subsequent elections, successors shall be elected in the manner provided by law for election of board members of the class to which the school district belongs.