"The Taoiseach (Irish word for Prime Minister) has invited the British Prime Minister to Dublin for talks on Northern Ireland and Brexit. Their offices are in contact to agree a date for these talks in the coming weeks," the spokesman said in a statement.
The statement said that the meeting would give both sides a better understanding of their respective positions.
However, it reiterated that the backstop and the Withdrawal Agreement are not up for discussion in the coming meeting.
It also indicated that the meeting will not discuss any changes to the political declaration as they are matters between the European Union (EU) and Britain.
The report about the agreed meeting between Johnson and Varadkar came after the latter raised the idea in a phone conversation about two weeks ago.
Johnson has insisted that he won't meet EU leaders for talks until the backstop is dropped. However, he has also promised that " under no circumstances" there will be a hard border on the island of Ireland.
The backstop refers to an arrangement with no time limit insisted by the EU side to avoid customs houses and other physical border infrastructure between Ireland and Britain's Northern Ireland after Britain's withdrawal from the EU, which Boris Johnson has vowed to deliver for the British pro-Brexit voters by the end of this October with or without a deal with the EU.