In her statement to the House of Commons, May said that Sir Tim Barrow had delivered her letter to Donald Tusk, President of the European Council, in Brussels.
"Today the government acts on the democratic will of the British people and it acts too on the clear and convincing position of this House," she said.
"Now is the time for us to come together, to be united," she said, a day after Scotland's parliament voted in favour of an independence referendum.
The formal notification to the other 27 EU members of Britain's intention to invoke Article 50 of the Lisbon Treaty was signed by May at her 10 Downing Street office last night.
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"After nine months the UK has delivered. #Brexit," Tusk tweeted on receiving May's letter. He later told reporters that there was no point pretending that it was a "happy" day and his approach would need to be one of "damage control".
"Paradoxically, there is also something positive in Brexit. It has made the community of remaining 27 members more determined and united," he said, adding that the negotiations ahead would be "difficult".
She promised to "represent every person in the whole United Kingdom" during the negotiations - including EU nationals, whose status after Brexit has yet to be settled.
"It is my fierce determination to get the right deal for every single person in this country. For, as we face the opportunities ahead of us on this momentous journey, our shared values, interests and ambitions can - and must - bring us together," she said.
"Instead, the referendum was a vote to restore, as we see it, our national self-determination. We are leaving the European Union, but we are not leaving Europe - and we want to remain committed partners and allies to our friends across the continent," her letter to Tusk reads.
"It is in the best interests of both the UK and the European Union that we should use the forthcoming process to deliver these objectives in a fair and orderly manner, and with as little disruption as possible on each side. We want to make sure that Europe remains strong and prosperous and is capable of projecting its values, leading in the world, and defending itself from security threats," it adds.
The focus will now shift to No.9 Downing Street in London, which houses the Department for Exiting the European Union headed by Brexit minister David Davis.
Following the notification process, the Great Repeal Bill will be published in Parliament tomorrow to cover the political break from the economic bloc.
On Friday, Tusk is expected to publish the European Council's negotiating guidelines, which will make the course of the so-called "divorce" proceedings for UK's exit clearer.
The notification of Article 50 marks the first formal step in the direction of Brexit after a referendum in June 2016 in favour of Britain leaving the EU.
Last night, the British PM spoke by telephone to Tusk, EU Commission president Jean-Claude Juncker and German Chancellor Angela Merkel to discuss the move.
Article 50 gives both sides two years to reach agreement, so unless both sides agree to extend the deadline for talks, the UK will have left the EU on March 29, 2019. The official negotiations with the EU are to begin by mid-May.
The UK has said it wants an "early agreement" to guarantee the rights of EU citizens living in the UK and those of British nationals living in EU countries.
Other issues which are likely to be discussed are things like cross-border security arrangements, the European Arrest Warrant, moving EU agencies which have their headquarters in the UK and the UK's contribution to pensions of EU civil servants - part of a wider so-called "divorce bill" which some reports have suggested could run up to 50 billion pounds.