Tim Barrow, the UK's ambassador to the EU, formally notified the office of EU Council President Donald Tusk on Monday.
On Wednesday next week May will formally notify Tusk by writing him a letter and then giving a statement to MPs in the UK Parliament.
A source at the UK Permanent Representation to the EU in Brussels said, "This meets the UK's longstanding commitment to trigger article 50 by the end of March 2017."
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Further comment came from secretary of state for exiting the European Union, David Davis, who 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.
Theresa May's official spokesperson said, "There will be a letter. We have always been clear we would trigger by the end of March and we have met that timetable."
He declined to comment on the contents of the letter or on whether there would be any further documents published next week.
In a tweet, European Council President Donald Tusk said, "Within 48 hours of the UK triggering article 50, I will present the draft Brexit guidelines to the EU27 member states."
A Commission spokesperson said, "Yes, we have been informed in advance, we are ready to begin negotiations.
"We are ready for the letter now we know it is to come on the 29th and yes, everything is ready on this side."
He added, "Then what will happen next, the first step after the notification will be the adoption of guidelines by the European Council, which is the political reaction.
"The European Commission will then immediately - and I mean immediately - issue a recommendation for the negotiations. This is the legal mandate and after this draft recommendation the European Council will formally adopt the mandate to the EU negotiator Michel Barnier."
Ukip leader Paul Nuttall said, "We welcome the long overdue announcement but regret it's nine month delay caused by political indecision, House of Lords betrayal and a number of legal challenges. It's late and we don't want to wait. Now let's crack on with it and stop procrastinating. It's time for Britain to go global."
David Martin, a UK S&D group MEP, said, "So 29 March is the day the UK formally starts its descent into the abyss. The article 50 process will certainly end one union and quite probably finish off the UK too. God bless all who sail in her."
Denis MacShane, the UK's former EU minister, told this website, "There is no surprise as No 10 has been saying end March is date to send in the article 50 letter. It is vital for May and the Tory party to ensure Nigel Farage and Ukip are not around after May 2019 when the real negotiations on trade, single market and all other than technical de-signing of EU treaty has happened."
Further comment came from European Green Party joint leaders Reinhard Bütikofer and Monica Frassoni who said, "It was a politically toxic mix of resentment, nostalgia, and open lies that produced a leave majority in the Brexit referendum.
"But in stitching together its strategy for leaving the EU, the British government has not only ignored the 48 per cent who wanted to stay and the overwhelming majorities against Brexit in Scotland, Northern Ireland and Gibraltar. It has also made fools of many Brexit supporters who would never have voted for the radical break with the EU that May is now advocating."
They continued, "May is pursuing a de facto coup against the majority of British citizens. Unfortunately, outside of Scotland there is no real opposition against the farce she is making of democracy, because Labour is happy not to play a role in this historic hour.
"Greens would prefer if the United Kingdom stayed in the EU. In case of Brexit, Greens would hope that the United Kingdom could stay united by allowing Scotland in particular to remain a fully integrated member of the European family of nations while England leaves the EU.
"It is in the in the hands of May and to a lesser degree of Jeremy Corbyn to foil both these hopes. It is in our hands as citizens of the EU27 to see to it that our European Union will not also fall victim to the gigantic folly of Brexit."