The officers of such district shall be a board of irrigation commissioners, consisting of a president, secretary and treasurer, and shall hold their offices for a period of one year. They shall be elected at an annual election to be held on the second Monday of December of each year, and shall hold their respective offices until their successors are elected and qualified. The board of county commissioners shall have power to appoint the first officers of such district, and such appointed officers shall hold their office until the next ensuing annual election, and until their successors are elected and qualified.