Upon the adoption of the resolution of consent by the city, such street or portion thereof within the city shall thereupon constitute a county highway. A certified copy of such resolution shall be filed with the board of supervisors. When the city council relinquishes an existing city street to the county, a certified copy of such resolution shall be recorded; and upon such recordation, all right, title and interest of the city in and to such portion of the city street shall vest in the county.