The Prime Minister's letter officially notifying the European Council of the UK's intention to quit will set in train a two-year negotiation process expected to lead to Britain leaving the EU on March 29 2019.
Britain's ambassador to the EU, Sir Tim Barrow, informed the office of European Council president Donald Tusk on Monday morning of the Prime Minister's plans.
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The announcement means that Mrs May will meet her self-imposed deadline of the end of March to get the withdrawal process under way.
She was cleared to take the step when the European Union (Notification of Withdrawal) Act gained royal assent last week, after a Supreme Court ruling forced her to seek the approval of both Houses of Parliament.
Mrs May will address MPs in a statement to the House of Commons following her regular weekly session of Prime Minister's Questions on March 29.
Mr Tusk has previously said he expects to release an initial response to the Article 50 notification within 48 hours, and an extraordinary summit of the remaining 27 EU member states is due to be called within four to six weeks.
That summit will draw up a mandate for the European Commission's chief negotiator, Michel Barnier, probably allowing talks to begin in earnest in May.
Notification of the historic step will come in the form of a letter from the Prime Minister to Mr Tusk, though Downing Street did not make clear whether this would be a physical letter handed to the European Council president by a UK representative or might be sent electronically.
It will be the first time that the provisions of Article 50 - which sets out the process for any EU member state "to withdraw from the Union in accordance with its own constitutional requirements" - have been activated.
Notification comes 279 days after the referendum of June 23 last year delivered a 52%-48% majority in favour of withdrawal.
Mrs May, who was visiting Swansea on Monday, is expected to conduct visits in all four nations of the UK before notification takes place.
The PM's official spokesman said: "Earlier this morning, the UK Permanent Representative to the EU informed the office of Donald Tusk that it is the UK's intention to trigger Article 50 on March 29.
"There will be a letter. She will notify President Tusk in writing. The Prime Minister will give a statement to Parliament as well.
"We have always been clear that we will trigger by the end of March and we have met that timetable."
The spokesman said Britain wanted to start withdrawal negotiations "promptly", but accepts that "it is right that the 27 have a chance to agree their position" before talks start.
Mr Tusk confirmed in a message on Twitter: "Within 48 hours of the UK triggering Article 50, I will present the draft Brexit guidelines to the EU27 member states."
Liberal Democrat leader Tim Farron said: "Theresa May is embarking on an extreme and divisive Brexit. She has rushed this through without a plan, and without a clue.
"On the day Theresa May is travelling the country claiming she wants to bring the United Kingdom together, she lets it be known she is about to unleash division and bitterness.
"Meanwhile, with the country in desperate need of an official Opposition, Labour has declared war on itself rather than defending the people from a hard Brexit. You can't have a rushed Brexit and a strong, united country."
Within 48 hours of the UK triggering Article 50, I will present the draft #Brexit guidelines to the EU27 Member States.— Donald Tusk (@eucopresident) March 20, 2017
Mr Farron repeated his call for voters to have the final say on the deal negotiated by Mrs May, arguing that departure from the European Single Market was not on the ballot paper in June.
The announcement on the timing of Article 50 comes shortly after European Commission president Jean-Claude Juncker warned that Britain may have to abandon its hopes of a trade deal if it rejects the terms offered by the EU - which are widely expected to include a "divorce bill" of as much as £50 billion.
The UK will have "the choice to eat what's on the table or not come to the table at all", Mr Juncker told German newspaper Bild am Sonntag.
Mr Juncker predicted that Britain's experience of withdrawal will bring the other 27 member states closer together, as they will "realise it's not worth leaving".
He said: "They will all see from the UK's example that leaving the EU is a bad idea. On the contrary, the remaining member states will fall in love with each other again and renew their vows with the European Union."
Secretary of State for Exiting the EU David Davis said: "Last June, the people of the UK made the historic decision to leave the EU. Next Wednesday, the Government will deliver on that decision and formally start the process by triggering Article 50.
"We are on the threshold of the most important negotiation for this country for a generation.
"The Government is clear in its aims: a deal that works for every nation and region of the UK and indeed for all of Europe - a new, positive partnership between the UK and our friends and allies in the European Union."
Mr Barnier was holding a "technical seminar" with representatives of the 27 remaining EU members to discuss the impact of Brexit on customs controls and procedures.
"EU27 have to start preparing now for future controls," he said.
Ukip leader Paul Nuttall said that, with a date set for notification, his party "must now ensure that PM delivers a clean Brexit with strong borders".
Scottish Government minister Michael Russell complained that the UK Government "somehow forgot to inform" the devolved administrations of the timetable for Article 50, leaving them to hear about it from the media.