In every municipality with a population of at least 5,000 and not more than 250,000 which is not subject to Division 1 of this Article, and in every municipality with a population of less than 5,000 which adopts this Division 2.1 as provided in Section 10-2.1-27, including in either event any municipality incorporated and existing under a special charter, the mayor of the city, with the consent of the city council or the president of the village or incorporated town, with the consent of the board of trustees, shall appoint a board of fire and police commissioners. This board shall consist of 3 members, whose terms of office shall be 3 years and until their respective successors are appointed and have qualified, except as provided in Section 10-2.1-2. No such appointment, however, shall be made by any mayor or president within 30 days before the expiration of his term of office.