The announcement was agreed on Thursday between Brexit minister David Davis and the European Commission's chief negotiator.
Brexit talks had been expected to begin in Brussels next week but May's loss of her parliamentary majority in a snap general election one week ago raised doubts about the date.
"The first round of talks that will see the United Kingdom leave the European Union will start on Monday June 19," the Department for Exiting the European Union ministry said on Thursday.
The announcement was agreed on Thursday between Brexit minister David Davis and the European Commission's chief negotiator Michel Barnier.
"We are starting," Barnier said on Twitter.
Since the general election, there has been growing pressure on May to moderate the government's approach and favour maintaining close ties with the European single market at the expense of controlling immigration.
The loss of her majority meant May has been reaching out to the ultra-conservative Democratic Unionist Party to prop up her Conservative party.
The Conservatives have reached a "broad agreement" with the DUP, a source told AFP on Thursday.
The source said talks with the small Northern Irish party were progressing well as meetings in Downing Street with all of the British province's main political leaders were taking place.
Conservatives and the DUP are committed to strengthening British unity, delivering Brexit, combating terrorism and delivering prosperity but "at the moment there isn't a deal," the source said.
The government meanwhile said the state opening of the parliament -- when May's government presents its legislation programme -- will take place on June 21, two days later than planned.
The Conservative source said this meant the party was "confident" it had enough votes for the programme to be approved, after May suffered a disastrous setback in snap elections a week ago that saw her lose her majority in the 650-seat House of Commons, just ahead of crucial Brexit negotiations with Brussels.
The Conservatives have 317 MPs while the DUP have 10.
The state opening will be followed by days of parliamentary debate and a confidence vote that will be the first major challenge for the new government.
Though on the surface, Thursday's meetings with Northern Irish parties were aimed at breaking the logjam in forming a new cross-party regional government in the province, May needs broader acceptance in the province of a Conservative-DUP deal.
Some fear the viability of Northern Ireland's fragile peace -- which has held since 1998 after decades of inter-community violence known as The Troubles -- could rest on the arrangement, with doubts around the UK government's impartiality.
"The risk is that Northern Ireland continues to fail to find solutions, and potentially the peace process unwinds," Simon Usherwood, senior politics lecturer at Surrey University, told AFP.
The 1998 peace accords in Northern Ireland set up a power-sharing executive in the British province, but this collapsed in January when Irish republicans Sinn Fein pulled out, citing a breakdown in trust.
An election in March saw the Protestant, pro-British DUP finish narrowly ahead of Catholic socialists Sinn Fein.
If the parties still cannot agree a deal by June 29, then the Northern Irish assembly's powers returned to the UK government.
Brexit is a complicating factor in the mix.
A majority in Northern Ireland wanted the UK to remain in the European Union, though the DUP backed a divorce from the bloc.
Northern Ireland's frontier with the Republic of Ireland will be the UK's only land border with the EU after Brexit.
London, Belfast, Dublin and Brussels all want to keep the border open, but no agreement has been reached.
The DUP and Sinn Fein are taking part in Thursday's talks at Downing Street, along with smaller parties.
Following the talks, Sinn Fein president Gerry Adams said the party would not stand for any Conservative-DUP arrangement which compromised British government impartiality in Northern Ireland.
"A little side bargain to keep Theresa May in power... won't have any integrity and certainly isn't as important as the needs of people" in Northern Ireland, said Adams.
"The prime minister has totally ignored the will of those people in terms of Brexit."