The regional board of education shall, after consultation with the local boards of education in the towns comprising the regional school district, determine the time and method by which the responsibility of conducting the educational program shall be transferred to the regional board of education, provided such transfer shall be completed within two years of the date of the organizational meeting of the regional board of education. When, in accordance with this section or section 10-47b, a regional board of education assumes the responsibility for administration of all programs which are provided in the member towns and are under the general supervision and control of the State Board of Education, the local boards of education are dissolved.