The Queen will sign the Article 50 Bill into law on Thursday, clearing the way for Theresa May to formally start talks to leave the European Union.
The European Union (Notification of Withdrawal) Bill was passed by MPs and peers on Monday, with royal assent the final stage in the process.
It will then be open to the Prime Minister to notify Brussels that the UK is leaving the EU, starting the two-year countdown to Brexit.
Mrs May has said she will invoke Article 50, the legal mechanism for withdrawal, by the end of the month in what will be a "defining moment" for the country.
She told MPs on Tuesday that royal assent was expected within the "coming days" and promised to come to the Commons later this month to announce when she had triggered Article 50.
Government sources indicated that royal assent was expected at 11am on Thursday.
The move comes after ministers were accused of "driving towards a cliff-edge with a blindfold on", as Brexit Secretary David Davis admitted they have made no assessment of the economic implications of failure to secure a deal with the rest of the EU.
The Prime Minister has declared her readiness to walk away from Brexit negotiations without agreement, insisting that "no deal is better than a bad deal".
And Foreign Secretary Boris Johnson said in a TV interview at the weekend it would be "perfectly okay" to crash out of the EU on World Trade Organisation (WTO) terms.
European Council president Donald Tusk said the signals coming from the UK Government just weeks ahead of the start of negotiations amounted to "threats", but insisted Brussels would not be "intimidated".
Failure to reach agreement on a future UK-EU relationship would be worse for Britain than for the remaining 27 states, he told the European Parliament.
Mr Davis tried to ease tensions with Brussels, urging colleagues to ensure future comments about the upcoming negotiations are "as calm as possible and as amicable as possible".
He issued a barely-veiled swipe at Mr Johnson, telling MPs on the Commons Exiting the EU Committee that he was preparing his strategy on the basis of "facts... not throwaway lines in interviews".
But he was unable to provide the committee with an estimate of the cost of "no deal", and said it might be a year before he could offer any figures.
Mr Davis confirmed that leaving under WTO rules would mean tariffs of 30-40% on agricultural exports and 10% on cars, the loss of EHIC health insurance cards for travellers and passporting rights for financial sector firms, as well as departure from the EU-US Open Skies arrangements for air transport.
But he said it will be possible to devise mitigating action in response to these issues.
"Any forecast you make depends on the mitigation you make, and therefore it would be rather otiose to do that forecast before we have concluded what mitigation is possible," said the Brexit Secretary.
Mrs May's "no deal is better than a bad deal" mantra was coined "in the emotional aftermath of the referendum (when) there were lots of threats of punishment deals", said Mr Davis.
"We had to be clear that we could actually manage this in such a way as to be better than a bad deal, and that is true.
"I can't quantify it for you yet. I may well be able to do so in a year's time.
"It's not as frightening as some people think, but it's not as simple as some people think."
Shadow Brexit secretary Sir Keir Starmer accused the Government of "recklessly talking up the idea of crashing out of the EU with no deal" while making no assessment of its potential cost.
Liberal Democrat Brexit committee member Alistair Carmichael said the Government's approach was "the equivalent of driving towards a cliff-edge with a blindfold on".
Mr Davis insisted a good Brexit deal was "eminently achievable" and said his impression from speaking to ministers from the remaining 27 member states was that "there is a growing determination to get a constructive outcome".
No deal would be "not as good an outcome as a free trade, friction-free, open agreement", he said.
On the potential stumbling block of a "divorce bill" of up to 60 billion euro (£52 billion) expected to be presented to the UK by Brussels, Mr Davis said that the UK had so far received no demand but was "a law-abiding nation" which would meet its obligations, while also insisting on its rights.
Holyrood's Brexit minister has insisted a fresh independence referendum is now the only way of protecting Scotland from the "hardest of Brexits".
Mike Russell said the Scottish Government had come to the view it was "hard to see" a deal being done with Westminster that would avoid another vote on leaving the UK.