Foreign Affairs Minister Simon Coveney says he hopes talk about the UK's departure from the EU 'will fade away' - and that Ireland 'defended itself against the vulnerabilities Brexit forced upon us.'
He is set to update the Cabinet on the proposed Brexit deal between the European Union and Britain on Tuesday.
The trade deal, struck on Christmas Eve, would see no tariffs or quotas on trade.
However the UK will lose access to several aspects of EU membership, including the Erasmus+ programme - which allows students to study in other states.
Mr Coveney has since confirmed that Ireland will pay to allow students in Northern Ireland access the programme.
Tweeting on St Stephen's Day, he said: "We promised we would do this and we will. NI students will have access to Erasmus+ if they want it post Brexit'.
The EU has published the document in full, which runs to some 2,000 pages.
On the deal itself, Mr Coveney says: "The border, the peace process, billions in tariffs and our place in the single market were all threatened by Brexit, these have all now been put to bed.
"When you weigh up the enormous damage of a no deal, I think Ireland has defended itself against the vulnerabilities Brexit forced upon us.
"The protection from the Irish protocol and this deal is beyond what many predicted would be possible."
'Relief tinged with regret'
He added: "There will still be some changes to the status quo on January 1st because of our nearest neighbour being outside the EU and cabinet will also discuss supports for the most affected sectors.
"This weekend my feeling is one of relief but tinged with regret that the UK is going it alone.
"Ireland is now focused on building a new relationship with the UK outside of the EU.
"Personally I hope talk of 'Brexit' will fade away."
President of the European Commission Ursula von der Leyen says: "It was worth fighting for this deal because we now have a fair and balanced agreement with the UK, which will protect our European interests, ensure fair competition, and provide much needed predictability for our fishing communities. Finally, we can leave Brexit behind us and look to the future.
"Europe is now moving on."
While the EU's chief negotiator Michel Barnier adds: "The protection of our interests has been front and centre throughout these negotiations and I am pleased that we have managed to do so.
"It is now for the European Parliament and the Council to have their say on this agreement."