Mr Varadkar said: "The further agreement yesterday provided additional clarity, reassurance and guarantees sought by some to eliminate doubts or fears, however unreal, that the goal was to trap the UK indefinitely in the backstop.
"It is not - these doubts and fears can be put to bed."
On Monday, Cabinet ministers in Dublin held emergency meetings to be briefed about the developments in Strasbourg.
The Taoiseach spoke with EU negotiator Jean-Claude Juncker on the phone during a break from his discussions with colleagues in Government Buildings.
Sinn Féin will be seeking confirmation from the Taoiseach in the Dáil today that the Withdrawal Agreement and Backstop have not been diminished or diluted in any way. https://t.co/xsqu3eUqEn
Mr Varadkar said the documents aimed to provide an additional layer of "interpretation, clarification and elaboration" to the UK ahead of the Westminster vote.
@duponline Arlene Foster tells @rtenews she will be talking to @theresa_may later. Mrs Foster says huge decisions have to be made and this is a pivotal moment. Decisions will be taken over the day.
"In the context of tonight's vote in Westminster, the outcome from yesterday's meeting with Prime Minister May and President Juncker is positive," he said.
"I hope and trust that the withdrawal agreement will now be endorsed by the House of Commons."
Mr Varadkar was due to fly to the United States on Monday evening for his annual St Patrick's celebration trip, but his plans were changed at the last minute to accommodate Monday's unscheduled cabinet meeting.