It is understood that Cullen, who became chairman of NZ Post after serving as Deputy Prime Minister under Helen Clark, is expected to become chairman of Auckland Transport when Lester Levy's term expires in November next year.
A senior source said three other chairs will be replaced when their terms expire next year: Panuku Development Auckland chairman Richard Aitken, Auckland Tourism, Events and Economic Development (Ateed) chairman David McConnell and Regional Facilities Auckland chairman Sir Don McKinnon.
King's appointment was made by the council's appointments and performance review committee on Monday. Todd Property managing director and former SkyCity boss Evan Davies has also been appointed to the board of Auckland Transport.
The appointments are due to be confirmed in the next couple of days.