There was speculation as to why Trump was kept on hold for a minute and a half before speaking with Varadkar.
This will be Varadkar's first official phone call with the US President since taking over the reins from Enda Kenny as Taoiseach.
Both leaders said they look forward to meeting in person.
Trump congratulated Varadkar on his "great victory" and said he feels like he knows all the Irish people in America.
The border between Northern Ireland, which is part of the United Kingdom, and the Republic of Ireland, an European Union member, will become the only land frontier between the UK and the European Union after Britain exits the bloc in March 2019.
During the conversation, some of which was recorded by RTÉ's Washington Correspondent & US Bureau Chief Caitriona Perry, and can be seen here, Trump also talked about his connections with Irish people based in the US.
The US president has spoken to the Taoiseach on the phone, for the first time since Mr Varadkar took office.
The Taoiseach also held a call with the UK Prime Minister, Theresa May, this afternoon in which they discussed the ongoing efforts to restore the Executive in Northern Ireland ahead of Thursday's deadline, and the supply and confidence agreement between the Conservative Party and the DUP.
However, when asked in the Dáil last week if he would rescind Mr. Kenny's invitation, Mr. Varadkar said he would not. However, he said no progress had been made in organising the visit and there was no timeline in place.
Mr. Varadkar will have his chance next March and before then if President Trump visits Ireland.