The bed tax was initially only applied to hotels and motels, but was extended to online businesses after tourism and business groups complained of unfairness.
Barnett said AirBnB was a modern response to tourists who were looking for new places to travel, stay and meet local people.
"Its pricing model allows new groups to travel and enjoy new locations that they may have been locked out of by the traditional accommodation providers," he said.
Auckland Council said the revenue from the new charges will fund half of Auckland Tourism, Events and Economic Development's budget for putting on major events and attracting visitors to the city.
It said it was careful to make the rates as fair as possible and noted that two-thirds of submissions on the charges were supportive.
The council last week released figures showing some AirBnB owners could make up to $80,000 a year if they rented out their property on a full-time basis.
Some Herald readers who rented out their properties said that did not reflect the various costs of managing a property.
They said that on top of mortgage costs and rates, they had to pay tax on any income and service fees to AirBnB. There were also costs for cleaning, upkeep of the property and gardens, on-call support, maintenance and repairs, water, power, and wifi.