He was speaking after a Brexit deal was reached in Brussels
The Taoiseach has said the deal on Brexit that guarantees no border between the North and Republic is ‘rock solid and cast iron.’
The agreement was hammered out late last night and announced in Brussels and Dublin this morning.
It now means talks can move on to the next phase of negotiations about trade.
Leo Varadkar said the deal will ensure there will be no physical infrastructure, related checks or controls on the Irish border.
He was speaking after European Commission President Jean-Claude Juncker and British Prime Minister Theresa May said "sufficient progress" had been made on the strict terms of the Brexit divorce.
Mr Varadkar said: "First of all, the Good Friday Agreement in all its parts is protected.
"Secondly everyone born in Northern Ireland will continue to have the right to Irish - and therefore EU - citizenship... third, the Common Travel Area will continue, allowing us to travel freely between Britain and Ireland.
"British and Irish citizens will continue to have the freedom to live work, study, access housing, healthcare pensions and welfare in each other's countries as if we were citizens of both."
On the border, he said: "There will be no physical infrastructure or related checks or controls."
Three options have been set out as to how this can be done, with Mr Varadkar adding: "Our preferred option is, of course, a deep and comprehensive agreement between the EU and the UK in its entirety - which will allow us to trade as we do now".
"However that might not be possible - so there is a backstop arrangement in place in which Northern Ireland, and perhaps all of the United Kingdom, will maintain full alignment with the rules of the internal market and customs union which are relevant to the avoidance of a border, North-South cooperation and the all-island economy.
"Sixth, people and businesses in Northern Ireland are being given the additional assurance that the United Kingdom government will ensure that Northern Ireland business will continue to have unfettered access to the whole of the UK, and that no new barriers will develop between Northern Ireland and Great Britain unless the Northern Ireland executive and assembly agree to it.
"Northern Ireland and Great Britain will not drift apart".
This evening, Sinn Fein's leader in the north, Michelle O'Neill, said she still had reservations about the agreement - and warned that the next stage of talks will be crucial:
“A lot of the text today is contradictory,” she said.
“There is much, much more work to be done and we are going to enter in to a very crucial second phase of talks.
“We need to make sure we stand up for all citizens’ rights.
“We need to make sure that we continue to make the case for special status and that includes remaining in the Customs Union and the Single market.”
Speaking in Brussels after overnight meetings, Mr Juncker said: "I will not hide that in between Monday and this morning we had a lot of talks: the prime minister and myself, the Taoiseach and myself, the Taoiseach and the prime minister.
"That's the reason why I would like to that the prime minister for (their) determination.
"We discussed the joint report agreed by the two negotiators - Prime Minister May assured me that it has (the) backing of the UK government.
"On that basis I believe we have now made the breakthrough we need.
"Today's result is of course a compromise".
"Both sides had to listen to each other, adjust their position and show willingness to compromise."
In her remarks, Mrs May said: "In Northern Ireland we will guarantee there'll be no hard border, and we will uphold the Belfast Agreement.
"And in doing so, we will continue to preserve the constitutional and economic integrity of the United Kingdom".
"Getting to this point has required give and take on both sides.
"I very much welcome the prospect of moving ahead to the next phase to talks about trade and security, and to discuss the positive and ambitious future relationship that is in all of our interests".
The DUP - which is propping up Mrs May's government in London - objected earlier this week to what is known as "regulatory alignment" between Northern Ireland and the Republic, which the party claimed would mean maintaining a soft border and a new frontier with the UK mainland in the Irish Sea.
In response to Friday morning's announcement, DUP leader Arlene Foster said: "Upon receipt of the draft text on Monday, the Democratic Unionist Party indicated to the Prime Minister that we could not support it as a basis for moving forward.
"Since then we have intensely engaged with the government right up until the early hours of this morning to secure changes to the document, mindful of the significant issues at stake for the future of Northern Ireland and the United Kingdom as a whole.
According to a statement from the DUP, contained within the new text are commitments that: