The board of police commissioners thus established under this chapter shall elect a chief of police and such other police officers as is or may be prescribed by the ordinance of such city. This power extends to unexpired as well as regular terms. The board shall also provide temporary police officers and policemen as occasion requires, such temporary police officers and policemen to be paid as may be prescribed by ordinance. The board shall have full and exclusive control and management of the police force of such city and shall have the power to discharge, suspend or fine the officers and members of the police force and to make and enforce rules and regulations for its government.