The planned new supreme court could cost up to £32m to set up, Lord Chancellor Lord Falconer has said.
Lord Falconer is overseeing the reforms
Unveiling details of a constitutional shake-up, Lord Falconer also revealed the new institution would take an estimated £10.8m to run each year.
Most of the money will come from the legal fees paid to the justice service, making all courts more expensive.
The supreme court is part of a plan to abolish the post of lord chancellor and set up a judicial appointments board.
The government has described the new Constitutional Reform Bill as a vitally needed modernisation.
The plans are widely expected to face stiff opposition both from Conservative peers and also from some senior members of the judiciary.
The new supreme court would replace the House of Lords as Britain's highest court.
New justices will have broadly the same power as the existing Law Lords, but crucially they will not sit in the second chamber.
Supreme court to replace House of Lords as highest court
New commission to appoint judges
Historic post of lord chancellor abolished
The government says the bill will clarify the relationship between government and the judiciary.
Lord Chief Justice Lord Woolf has suggested the new supreme court will cost £50m and has threatened to oppose the plans unless there is "new money".
Publishing the bill on Wednesday, Lord Falconer said the costs of setting up the court would depend on which building was chosen.
Suggestions include the Middlesex Guildhall, near the House of Commons.
The minister admitted he could not say when the court would be up and running and said it was possible it might be delayed until a new building was found.
If that took too long, the court would still have to sit in the House of Lords.
Tory constitutional affairs spokesman Alan Duncan said the bill was both "unnecessary and unwanted".
"Labour think that something must be bad because it is old," said Mr Duncan.
Tory Alan Duncan says the plans are unnecessary
"They don't realise that it might be old because it is good."
Liberal Democrat constitutional affairs spokesman David Heath complained of "haste and incompetence" in the government's handling of the reforms.
He backed the principles behind the changes but wanted to ensure the plans protected judicial independence.
Lord Falconer - who will be the last lord chancellor if the bill is passed - insisted the reform was necessary before the current arrangements broke down.
He told BBC Radio 4's Today programme. his job raised the prospect of a potential conflict of interest as he had the dual role as top judge and a cabinet minister.
"Let the politicians do the thing that the politician does, let the lord chief justice, who is the chief judge in the country, become recognised as the chief judge and do it before the arrangement breaks down," he said.
Lord Falconer said he would have "limited powers" to challenge any recommendation from the new appointments commission.
But the times he expected to veto an appointment would be "very, very rare indeed".
Former Master of the Rolls Lord Donaldson said the current system worked perfectly well and there was enormous concern in some sections of the House of Lords over the plans.
The proposals were unveiled in a surprise announcement at the time of last summer's cabinet reshuffle.