Responding to the resignation of Auckland Transport chair Adrienne Young-Cooper only hours after his election victory on Saturday, Brown said it was "very good" and he respected her for it.
Asked about a statement from the remaining board members saying they plan to stay on, he said "everyone remains for a little bit".
He spoke of an interim period of "weeks" for the remaining directors, saying he wanted to discuss the matter with the new councillors, many of whom he had not yet met.
Asked which directors he was addressing and what is their future, Brown said: "I made it very clear I was keen to take back some controls, which means they have a clear direction of what they do and the types of people appointed to it."
In a statement, AT's remaining board members said they will remain in place while any review of the board, current appointments and arrangements are progressed and managed transitions confirmed for any new members.
"The Auckland Transport Board recognise the requirement to maintain an appointed Board to provide continuity, so that AT can operate legally and constitutionally. It's also important that the Board is in place to guide the leadership team during the current transition," the statement said.
Deputy chairman Wayne Donnelly has taken on the role of acting chairman.
"The Board looks forward to engaging with the Mayor-Elect and the Council-Elect on the future direction for transport in Auckland.
"We wish to acknowledge the significant contribution to Auckland, and to the leadership of the Board, provided by the retiring Chair, Adrienne Young-Cooper," the directors' statement said.
'Auckland's got to get its mojo back'
Auckland Business Chamber chief executive Simon Bridges told RNZ's Morning Report the new mayor and council was a chance for a re-set.
"The guy's got empathy for the private sector I think you've got a guy who wants to harness and unleash business. That's music to our ears.
"Wayne Brown is a rough diamond but if he can channel that into being Auckland's rough diamond in a way Mayor Goff perhaps didn't, particularly around business issues that'd be very welcome indeed.
"There's just this general ... malaise or sense that Auckland's got to get its mojo back."
Viv Beck, whose decision to pull out of the mayoralty race helped secure a centre-right win, told RNZ's Morning Report she did not discuss her intention to withdraw with Brown.
Beck, who returns to her role as Heart of the City chief executive, said the move to the centre right in council and at local board level would be positive for business.
The Covid-19 recovery needed a much more aligned effort between central and local government, the private sector and the not-for-profit social sector, and the election result sent a strong signal to the Government, she told the broadcaster.
She hopes central city businesses won't need to fight so hard with council over issues affecting them, such as construction.
Bird's eye view
Brown spent his first day in the job surveilling the "realm" in a helicopter.
Brown did his best to stay out of the limelight, cancelling a number of media interviews, to spend time with his family before beginning the business of running the country's biggest city today.
However, he did find time for a family photograph at Western Park in Ponsonby and a few words with the Herald before contemplating a quick trip to Piha, where he likes to surf, but admitted to being a "bit dusty" after Saturday night.
Yesterday, the incoming mayor, his son and his partner spent 90 minutes in the morning cleaning up the mess from a party the night before at Ponsonby Central.
Then it was time to "survey the realm" in a friend's new helicopter, heading west to Piha where the "surf was bloody good... and dozens of surfers everywhere".
He flew to the edge of the Kaipara Harbour and followed the rail line back to Helensville and the growth areas of Kumeu and across Hobsonville Point, getting a bird's eye view of the "amazing growth in the northwest" with lots of spare land for more housing.
"And you think, what a shame we are putting houses on the Pukekohe soils. You look out around Kumeu, scrape off that much topsoil [he indicates a few inches] and it's yellow clay," Brown said.
He said the city looked beautiful but there were some ugly bits, pointing to blocks of crowded houses at Karaka jammed up, told not to have car parks, and no bus service.
"How did that happen?" said Brown, who pledged to "Fix Auckland", including infrastructure and taking back control of the council-controlled organisations (CCOs), in particular Auckland Transport.
Only hours after Brown's emphatic win over Labour councillor Efeso Collins, AT chairwoman Adrienne Young-Copper resigned immediately in response to a call from the new mayor for the whole board to step down.
"It is clear that the mayor-designate wants a clear runway," Young-Cooper said in a statement. "I willingly exit the role."
In an exclusive letter to Aucklanders written for the Herald on Sunday, Brown said there is no agency about which the Super City dwellers are angrier.
"I think the board of directors should heed the message from the election and offer to resign," he said.
Just 31 per cent of Auckland's nearly 1.2 million eligible voters took part in this year's local elections
Brown will today spend most of the day being briefed on the council's books, its economic forecasts over the next three years, and all contingent liabilities and other risks.
The briefing will also include the finances of the four CCOs and other entities in which ratepayers have an interest.
Brown may issue a statement later in the day on the state of the council's finances.
This week, Brown also plans to meet with all 20 councillors to congratulate them in person and to discuss how they can best help deliver the change Auckland voters have demanded.
He also intends to meet with the leadership of the Independent Māori Statutory Board, and with his main mayoral rival and former Manukau councillor, Collins, to discuss how they can help contribute to the change Aucklanders have voted for.
Collins said he was always open to meeting with Brown, adding he had spoken to him yesterday afternoon "where I again offered my congratulations".