This will include greater oversight and control by councillors of the mayor and his office, which has wide powers, a $4 million budget and up to six spin doctors.
The actions against Mr Brown were decided on after a meeting at the Auckland Town Hall lasting more than five hours.
The mayor attended for the first 90 minutes and gave councillors a full and unconditional apology.
Councillor Chris Fletcher said the apology was "most sincere". In a statement, Mr Brown said: "I understand the frustration and disappointment that councillors feel.
"I realise that I have a good deal of work to regain their trust and rebuild our working relationships in the interests of Auckland. This is my focus, starting today."
Mr Brown did not respond to the councillors' set of actions for Thursday.
Many councillors spoken to after the meeting said they were reserving until then their judgment on Mr Brown's ability to lead the city. Mike Lee, Alf Filipaina and Arthur Anae support the mayor staying.
If councillors are still not happy with Mr Brown's response after Thursday, they retain the ability to pass a vote of no confidence in him.
Deputy Mayor Penny Hulse said councillors expressed to Mr Brown their profound disappointment and disapproval of his actions with regard to his conduct and undeclared conflicts of interest and the damage to Auckland's reputation.
Asked if Mr Brown should continue in the job, Mrs Hulse, Mr Brown's deputy for three years, said: "It's his decision to stand down or remain there."
Mr Brown has been in the spotlight since intimate details of his affair with Bevan Chuang were revealed.
A report by EY (Ernst & Young) cleared him of using council resources or providing preferential treatment in connection with the affair, but found he failed to declare more than $39,000 in free hotel rooms and upgrades.
The hotels were paid for by Mr Brown and his family for their private use, but he failed to declare them as required under the council code of conduct.
Next steps
Recommendation for Thursday's council meeting
*The governing body receives the independent review (the EY report) commissioned by the chief executive.
*The governing body expresses its profound disappointment and disapproval of the mayor's inappropriate conduct and undeclared conflicts of interest, which are the subject of the report and which have caused damage to Auckland Council's reputation and widespread concern among the public.
*Accordingly the governing body censures the mayor for his behaviour that in the view of the governing body breaches the council's code of conduct.
*The governing body requests that the mayor make full reimbursement of all remaining personal costs and also make an appropriate contribution to other costs incurred by the council.
*The governing body requests the incoming chief executive, in consultation with the office of the Auditor-General, to review the process for managing and overseeing members' interests both in the mayoral office and with elected members.
*The governing body now signals its willingness to work with the mayor and establish better liaison between the mayor's office and governing body in the best interests of Auckland and its people.
