She is also no longer the Minister Responsible for the Earthquake Commission.
David Parker's Economic Development portfolio was given to Twyford.
Nanaia Mahuta has been given the associate Minister of Housing (Maori Housing) portfolio.
Ardern would not comment on impending changes to Kiwibuild, saying she would leave it for the reset announcement.
Ardern said the new housing Ministers were not an admission that Twyford had failed, but that is was a job for more than one minister.
She said a lot had gone right in housing, such as state housing, but many things had gone wrong and that was why other ministers had been brought in.
Woods and Faafoi would bring a fresh perspective into housing, Ardern said.
She defended Twyford and said he had pursued an "extensive housing agenda".
Grant Robertson becomes Minister Responsible for the Earthquake Commission, Jenny Salesa becomes Minister of Customs, Peeni Henare becomes Minister of Civil Defence and a small number of associate delegations change.
Ruth Dyson will be nominated for the role of Assistant Speaker.
Michael Wood becomes the Senior Government Whip and gives up his roles as Parliamentary Under Secretary to the Minister for Ethnic Communities and Chair of the Finance and Expenditure Select Committee.
Poto Williams will become a Minister outside Cabinet.
Priyanca Radhakrishnan becomes the Parliamentary Private Secretary for Ethnic Affairs.
Willow Jean Prime becomes Parliamentary Private Secretary for Local Government.
Ardern said while ministers were in the middle of major projects, she wasn't looking to major changes.
She said Faafoi had done an "outstanding job" and described him as a trusted pair of hands.
"It was an admission it was a huge job … There was no template, no blueprint for what we were doing here."
She had been working on the changes for Twyford for "some time".
Ardern said she was disappointed about the number of women in Cabinet. "Making sure we improve those numbers is important to me."
"I don't believe we will lose momentum because that momentum has continued," she said. She said it was "not the right time" for Meka Whaitiri to be placed back into Cabinet.