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All but Cr Gerry Eckhoff voted in favour of the building, touted as an "interim" measure.
Crs Doug Brown, Gretchen Robertson and Duncan Butcher were not at the meeting.
Chairman Stephen Woodhead said after the meeting the $926,000 price tag for a purpose-built facility included $609,000 for the estimated cost of the "general build", with an additional $174,875 for civil defence requirements and $141,139 for the council chamber.
"No doubt the tender process will bring in a sharp tender [price]."
The building needed to be suitable for three to five years and required new utility services, as well as data-cabling, fire doors, disabled access, toilets and kitchen facilities, which all "came at a cost", he said.
"We're not putting up a house and it's not cheaply done."
The benefits of holding meetings back on its Stafford St site - the ORC has, since May, been holding public meetings in the Salvation Army premises in Princes St - would be "enormous".
Holding the meetings in Princes St had highlighted the difficulties of being off-site, including set-up and close-down time required of staff, Mr Woodhead said.
Opposing the proposed facility, Cr Eckhoff said he could not accept spending $1 million for a "bit of convenience" when the facility councillors were using was fine.
But his view was not shared by others, including Cr Michael Deaker, who said the price was " not too bad".
While the temporary building would not be relocatable, it could be dismantled, so cost recovery was possible when it was no longer needed.
"We won't regret doing this, even in five years' time."
Cr Bryan Scott said it was time to "get on with it". Providing a multipurpose facility for council, staff and civil defence capability was a step forward.
"It's a good idea. One million dollars is not insignificant, but if you look at the previous proposal [a $31 million waterfront building, put on hold in 2009] this is only 3% of that. It is the reality of doing business."
Cr David Shepherd said the Princes St facility was not ideal and had not been tested by a major hearing, which could turn out to be a "nightmare".
"It's a no-brainer; let's get on with it."
Cr Trevor Kempton agreed, while Cr Sam Neil said he now supported the proposal, having previously voting against moving off-site.
The councillors agreed for architects Oakley Gray to finish the design and for construction and fit-out tenders to be called for.