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He is due to give a speech at Queen's University, Belfast, on the future of north-south relations.
In the afternoon, he will hold meetings with local political parties.
On Saturday, Mr Varadkar, who is the Republic of Ireland's first openly gay taoiseach, will attend a breakfast event as part of Belfast's gay pride festival.
The taoiseach will meet the DUP, Sinn Féin, the SDLP and the Alliance Party on Friday. He will not be meeting with the Ulster Unionist Party as its leadership was not available.
Leo Varadkar has already ensured his first trip over the border as taoiseach will be one to remember.
His decision to attend the gay pride breakfast gathering as the Republic's first openly gay Taoiseach is sure to grab the headlines on Saturday.
But, it will be his speech at Queen's University and his meeting with the DUP, in particular, that will be the main focus on Friday.
That's because the DUP this week accused the taoiseach of engaging in megaphone diplomacy and being unhelpful when he suggested Brexit supporters should be the ones to design a new border.
His meeting with DUP leader Arlene Foster will come days after a row between the DUP and the taoiseach over the Irish border post-Brexit.
Mr Varadkar had said he would not design a border for Brexiteers but DUP MP Jeffrey Donaldson said that "megaphone diplomacy from Dublin" would not sort out the border issue.
On Thursday, former taoiseach John Bruton, who was also a former leader of Mr Varadkar's Fine Gael party, said that the DUP is in a position to answer questions over Brexit because of its Westminster pact with the Conservative Party.
"Do they (the UK government) want to leave the customs union? Are they willing to accept being in the European Economic Area? What type of agriculture policy will the UK government pursue post-Brexit?
"These are all questions that Arlene Foster is in a position to answer because she's critical to the continuance of the current UK government."