Theresa May will trigger EU withdrawal talks under Article 50 on March 29, Downing Street said.
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.
Downing Street said she "will be engaging and listening to people from right across the nation as we prepare to leave the EU as one United Kingdom."
Before starting the tour Mrs May said: “From my first day on the steps of Downing Street, I made clear my determination to strengthen and sustain the precious union.
"I have also been clear that as we leave the European Union I will work to deliver a deal that works for the whole of the UK."