The council's Customer Service Centre and the Tauranga Library would remain open as normal.
City transformation committee chair Larry Baldock thanked the community for their patience during the deconstruction and demolition.
"We are on a journey to become an internationally competitive city, and revitalising our city centre and our waterfront is a key component to this," he said.
"The demolition of the old administration building is a short term disruption for long term gain."
The demolition can be viewed from a web cam feed on the council's website.
Council was partnering with Little Big Events to activate the space once the building was demolished and the site had been cleared.
"Our Place" will be a temporary addition to the city centre until investment decisions were made on the future of the space and the site was developed.
The council resolved in September 2016, as part of a Long Term Plan amendment, to demolish the administration building as soon as possible following the discovery of toxic mould in the building in November 2014.