Brexit director David Davis welcomed the move, saying it marked the next essential step in ensuring that Britain is ready for life after leaving the European Union next March.
The Queen's signature in the European Union Withdrawal Bill means it is now official British legislation.
The act gives Prime Minister Theresa May's government the power to transfer thousands of pieces of EU legislation into British law after Brexit.
The law will also repeal the 1972 European Communities Act, which took Britain into the EU and meant that European law took precedence over laws passed in the UK Parliament.
The so-called Brexit bill endured a roller-coaster ride as it went through the legislative and parliamentary processes in both the House of Commons and the House of Lords.
Members in the unelected upper chamber voted in favor of a number of amendments, threatening the success of May's Brexit bill, described as the most important new law since the end of World War II.
The Speaker of the House of Commons, John Bercow, announced at the start of Tuesday's session, that the Brexit bill had been signed by the Queen. His announcement was greeted with a loud cheer from Members of Parliament, while a similar announcement was made in the House of Lords.
Brexit Secretary David Davis described the Royal Assent as a landmark moment in Britain's preparations for leaving the European Union.
He said the historic act will make sure the UK's laws, entwined with over 40 years of EU law, will continue to work from the day Britain leaves, ensuring a smooth and orderly exit.
It does that by transferring EU law into British law where appropriate and creating temporary powers to correct the laws that will no longer operate appropriately.
Davis said: "The EU (Withdrawal) Act is a vital piece of legislation that will ensure we have a functioning statute book for exit. Since the Bill was introduced in Parliament last year, MPs and peers have spent more than 250 hours debating its contents and more than 1,400 amendments have been tabled.
"We will now begin the work of preparing our statute book, using the provisions in this Act, to ensure we are ready for any scenario, giving people and businesses the certainty they need."
A spokesperson at the Brexit office told media: "In total, it's expected that around 800 pieces of secondary legislation will be needed. Alongside this program of secondary legislation, departments are delivering on a further package of bills which will deliver the more significant policy changes needed as a result of our exit from the EU."
The Brexit journey is far from over with more pieces of legislation related to Britain's withdrawal waiting to enter the parliamentary process.