The change in office shall be made as follows: the Mayor and City Council shall meet at the regular meeting in December each year and the outgoing officers and the outgoing members of the Council shall present their reports, and upon the old Council having completed its business up to the said time, the outgoing members of the Council shall surrender their offices to the incoming members, and the outgoing members shall, thereupon, each surrender to his or her successor in office all property, records, papers and moneys belonging to the same.