Draft legislation paving the way for a multi-billion pound restoration of the Palace of Westminster will be published "shortly", MPs have been told.
Commons leader Andrea Leadsom said it was still the plan for the site to be largely vacated by the mid-2020s after MPs approved the move in January.
Work on a three-year business plan for the comprehensive refit is under way and should be completed by mid 2021.
MPs would have "fulsome" time to scrutinise the plans, Mrs Leadsom said.
Giving evidence to the Commons Finance Committee, she said she would like the public to continue to have access to the site during the works, including tours of the Elizabeth Clock Tower and possibly Westminster Hall.
MPs voted in January to leave the historic site, home to both Houses of Parliament, for a "significant" period of time to make way for a massive restoration and renewal programme.
The iconic building, which was rebuilt in the 19th Century after it burnt down, faces a number of "critical risks", including the chance of another catastrophic fire due to its outdated electrical systems.
Its sewage system is also antiquated and parts of the site are riddled with asbestos.
The Commons has agreed to a "full and timely" move to another location as part of the proposed modernisation, although this will not take effect until 2025 at the earliest and it is not yet clear where MPs and peers may decamp to.
Updating MPs on progress in the past nine months, Mrs Leadsom said she expected to publish draft legislation soon which would establish a sponsor board to oversee the project, a delivery authority to manage it and an estimates commission to approve the funding.
She said a joint select committee of MPs and peers would be set up to scrutinise the bill and to sign off the design and budget for the project.
The National Audit Office and the Public Accounts Committee, she added, would also be expected to take a close interest in the "hugely expensive" project to ensure value for money.
"The opportunity is there to scrutinise significantly at all levels," she said.
A review by accountants Deloitte in 2014 estimated the cost of repairing the building if both the Commons and Lords moved to alternative venues would be between £3.5bn and £3.9bn,
In contrast, the bill for a partial decant would be between £3.9bn and £4.4bn and a rolling programme of works, with Commons and Lords chambers being "vacated and then re-occupied", up to £5.67bn.
Mrs Leadsom said a lot of other maintenance work was taking place in the meantime.
But Labour MP Chris Bryant, chair of the committee, said this was happening too slowly, pointing out it had taken 12 years alone to decide on new lights in Westminster Hall, the oldest part of the building.