Five new councillors were sworn in - Efeso Collins (Manukau), Richard Hills (North Shore), Daniel Newman (Manurewa-Papakura), Greg Sayers (Rodney) and Desley Simpson (Orakei).
Goff said the council would work in the best interests of Aucklanders and doing what is just and fair.
Borrowing a slogan from his successful campaign, which he won on October 9, he pledged to build a city where all people get the opportunities they deserve to reach their full potential - "and that no one is left behind".
Goff said that in just over a decade Auckland would add half a million people to its population.
"It is critical that we have the infrastructure in place to service the needs of these new residents.
"Infrastructure has lagged behind growth and affected the quality of our lives.
"With 800 new cars registered every week in Auckland, our roads have become more and more congested and gridlocked.
"Demand for housing is outpacing supply. House prices and rents have skyrocketed.
Auckland has secured a title we did not want - the fourth least affordable city in the world."
Goff said Aucklanders want bold action to address the housing crisis.
"Each night hundreds of people sleep rough around the city. Kids are living in cars.
"Families are sleeping in garages. This is not the decent society we want our city to be.
"We want our children to grow up in an inclusive and fair community and that starts with secure, affordable and healthy homes."
On transport, he said there are encouraging developments.
"Last Saturday, I opened the new Otahuhu bus and railway station with Transport Minister Simon Bridges.
"It symbolises a new era of a modern and integrated public transport system. That is what we need to help decongest our roads.
"The City Rail Link will help too when it comes on line in 2023.
"No great city ever built its way out of congestion by simply relying on new roads," he said.
The evening included performances by the Auckland Philharmonia Orchestra, Auckland Choral and the Stellar Singers.
