The Taoiseach has told the Seanad that Ireland's ability to advance its national interests and exert its influence - both within and beyond the EU - has never been more important.
Mr Varadkar was addressing Senators on the 70th anniversary of the Republic coming into effect.
"Becoming a Republic changed Ireland's relationship with Britain, it resolved a number of constitutional issues, some significant, some symbolic, and it enabled us to engage with the world in a different way.
"It was an important stepping stone on the way to our country taking its place among the nations of the world," said Mr Varadkar.
The first Dáil Éireann declared Ireland independent on 21 January 1919.
The Irish Free State was formally created on 6 December 1922, but the 26 counties of Ireland did not officially become a republic until midnight on Easter Sunday, 17 April 1949.
Mr Varadkar thanked Senators for their co-operation in passing the Omnibus legislation to prepare Ireland in the event of a no-deal Brexit.
Mr Varadkar told the Seanad that the Withdrawal Agreement contained a commitment from the UK that Brexit will not result in any diminution of the rights, safeguards and equality of opportunity as set out in the Good Friday Agreement.
"I have discussed with Prime Minister [Theresa] May the responsibilities of the UK government under the Good Friday Agreement, with or without a deal."
He also said that Irish citizens in Northern Ireland will continue to be European citizens in all circumstances.
"They will continue to enjoy the right to travel and work and study freely throughout the EU, benefiting from the important rights not to be discriminated against on the grounds of nationality while doing so."
"The Common Travel Area will also be maintained in all circumstances," he said.
#OnThisDay in 1949 the Republic of Ireland Act 1948, signed into law by President Seán T. Ó Ceallaigh on 21 December 1948, came into force, formally ending the statutory role of the British monarchy in Ireland.https://t.co/otzVNU2t2U pic.twitter.com/AyrFN0kcA0— President of Ireland (@PresidentIRL) April 18, 2019
Mr Varadkar said the Government was working to deepen "Ireland's influence within the EU, influence the debate on the Future of Europe, and diversify our trade with the wider world".
"We have an ambitious vision of our role in the world. So, we launched the Global Ireland initiative, which aims to double the scope, and impact, of Ireland's global footprint by 2025," said Mr Varadkar.
He said this was something we should be doing even if there was no Brexit.