Whenever, by extension of its territorial limits as aforesaid, new territory is annexed to such city, the lawmaking authorities thereof shall, by ordinance, organize the same into a new ward or wards, or attach the same to some existing ward or wards, long enough before the next ensuing general city election to enable electors in such annexed territory to register, and all other proper steps to be taken according to law, so that the electors of such annexed territory may have full opportunity to register and vote at such election. Actual residents of any territory at the time of the annexation thereof as aforesaid shall, if otherwise qualified, be qualified electors of such city, and be eligible to any office therein at the next general city election following such annexation.