The politicians are due to discuss developments on Brexit, including the future of the Irish border, the Common Travel Area and provisions to ensure the peace process is protected.
The visit will be Mr Varadkar's first meeting with the prime minister since her keynote Brexit speech in Florence last Friday.
In it, Ms May reaffirmed her commitment to the Good Friday Agreement, as well as ensuring no physical border infrastructure is put in place along the Irish border after the UK's withdrawal from the EU.
Following her speech, Mr Varadkar said: "I'd give the speech a cautious welcome. I think it is a genuine effort by the prime minister to move things along and make progress."
Mr Varadkar is also due to take part in Ireland's 2023 Rugby World Cup bid during his visit.
