The City Council shall have the power by ordinance to fix the boundary limits of the City and to provide for the alteration and extension of said boundary limits, the annexation of additional territory lying adjacent to the City, and the detachment or disannexation of territory, with or without the consent of the owners and inhabitants of the territory annexed, detached, or disannexed, in any manner not inconsistent with applicable procedural rules prescribed by Law. Upon final passage of any ordinance annexing territory, the corporate limits of the City shall thereafter include the territory annexed; and when any additional territory has been annexed, the same shall be a part of the City and the property situated therein shall be subject to taxes levied by the City; and the inhabitants thereof shall be entitled to all of the rights and privileges of all citizens, and shall be bound by this Charter and the ordinances, resolutions, rules and regulations of the City. Upon the final passage of any ordinance detaching or disannexing territory from the City, the corporate limits of the City shall be reduced by the territory detached or disannexed.