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The plan includes a new six-storey building behind Parliament House on Museum St which is currently used as a carpark but owned by the Crown.
It would have a direct link to Parliament House.
The Executive Wing annexe previously occupied by the Press Gallery and considered an earthquake risk would also be replaced.
House Speaker Trevor Mallard said funding would be sought in the 2022 budget and work was expected to begin later that year.
"What you're seeing is something that's designed to have the buildings of Parliament owned by the people of New Zealand."
The project is expected to cost more than $200 million.
Mallard said owning the buildings was better than leasing office space.
"Just the whole idea - you have a Parliament [and] you had got the core of your constitutional buildings owned offshore - doesn't sit very well with a lot of people. This is a long term control question."
The plans were "a bit plainer" than what speaker David Carter announced in 2016, when the budget was $100m, but there was an extra building and inflation to take into account.
Mallard said the overall cost should not be more than two cycles of the 15-year lease paid to rent Bowen House but it was logical to have a long term view on owning Parliament buildings.
He would not say what the lease was for Bowen House, which was not being used due to it being earthquake-prone.
Mallard was hopeful there would not be politicking and said there was cross-party support for the plan.
He said there were some heritage concerns with the annexe but there was a plan B if it could not be demolished, which would involve "low-level strengthening" and using the space for storage.
The goal is to have the work completed by 2026.