Officially known as the European Union (Notification of Withdrawal) Bill, it passed the Parliamentary process following votes in the Commons and Lords on Monday.
When it becomes law, the Prime Minister is free to decide when to invoke the two-year negotiation period for Britain to leave the EU.
Downing Street has suggested this is not likely until the last week of March.
Royal Assent nowadays is generally declared to both Houses by their Speakers and is listed in Hansard, the official record of proceedings in Parliament.
After this, the bill becomes part of the law of the land and is known as an Act of Parliament.
Government sources say Royal Assent is likely to be granted at around 11am.
It has not been refused since 1707, when Queen Anne refused it for a Bill for settling the militia in Scotland.
The bill's passing into law follows a difficult day for the Government in which ministers were accused of "driving towards a cliff-edge with a blindfold on".
Brexit Secretary David Davis was forced to admit his department has not made an assessment of the economic implications of failure to secure an agreement with the rest of the EU.
His admission was despite the Prime Minister repeatedly saying she thinks no deal is better than a bad deal.