The Prime Minister has triggered Article 50 after her letter to European Council President Donald Tusk was delivered by Ambassador Sir Tim Barrow in Brussels.
Mr Tusk immediately responded on Twitter: "After nine months the UK has delivered. #Brexit."
Kicking off the two-year process of withdrawal from the European Union, Theresa May told MPs: "This is a historic moment from which there can be no turning back."
The PM accepted it was "a day of celebration for some and disappointment for others".
But she added: "Now is the time for us to come together, to be united across this House and across this country to ensure that we work for the best possible deal for the UK and the best possible future for us all."
She pledged to deliver "the democratic will of the British people" and to take the "unique opportunity" to "shape a brighter future" for the UK, adding: "I choose to believe in Britain and that our best days lie ahead."
Under the terms of the Lisbon Treaty, a two-year period of talks with the 27 remaining EU member states lies ahead.
After marking out hard lines on future payments to the European Union and the influence of EU law after Brexit, the text of the Prime Minister's letter offered some room for manoeuvre in negotiations.
Mrs May struck a note of conciliation, insisting: "We are leaving the European Union, but we are not leaving Europe - as we want to remain committed partners and allies to our friends across the continent."
But she said a UK exit without a deal "is not the outcome that either side should seek".
Mr Tusk told a news conference shortly after being handed the Article 50 notice: "There is no reason to pretend that this is a happy day, neither in Brussels nor in London.
"After all most Europeans, including almost half the British voters, wish that we would stay together, not drift apart.
"But, paradoxically, there is also something positive in Brexit.
"Brexit has made us, the community of 27, more determined and more united than before."
And in a personal message to Britain he added: "We already miss you. Thank you and goodbye."
The European Commission, Council and Parliament have signalled that "EU law must apply until Brexit day" - when Britain officially leaves.
The European Parliament, which can veto a UK-EU deal, is next week expected to make the guarantee of full EU citizen rights a red line - a potential sticking point which Mrs May has highlighted as a "priority" for the talks ahead.
While Mrs May wants to negotiate a new trade deal with Europe alongside the divorce settlement, the EU has said it is reluctant to do so until after the UK has officially left.
Angela Merkel has rebuffed Mrs May's call for negotiations on Britain's withdrawal to run alongside talks on a trade deal.
The German Chancellor said: "The negotiations must first clarify how we will disentangle our interlinked relationship... and only when this question is dealt with, can we, hopefully soon after, begin talking about our future relationship."
The Commission chose the morning of the Article 50 declaration to formally block a key merger between the London Stock exchange and its German counterpart the Deutsche Borse.
Some influential commentators believe this decision was a key test of the EU's attitude to negotiations with the UK.
The pound pushed higher against the euro as the starting gun on Britain's formal exit from the EU was fired, climbing from a rise of 0.2% to 0.6% by the time the PM had finished addressing Parliament. There was little movement against the dollar.
"Today's the day the impossible dream came true. I'm delighted," former UKIP leader Nigel Farage told Sky News, while enjoying a pint in central London.
North of the English border, however, a day after MSPs backed a second Scottish independence vote, First Minister Nicola Sturgeon tweeted ahead of the declaration: "Today, the PM will take the UK over a cliff with no idea of the landing place. Scotland didn't vote for it and our voice has been ignored."