The EU summit is set to take place in Brussels on Tuesday and Ireland will be the first country to sign the deal.
The prime minister, Leo Varadkar, has said that the deal is a “once-in-a-generation opportunity” and said it will help Ireland “get out of this mess”.
Ireland has also been accused of dragging its feet on the deal because it has had a “lack of political will”.
“We are confident that we will have a positive outcome and we are hopeful that we can have a deal at this summit,” Mr Varadker said.
“It will allow Ireland to move forward on our economic reform and its a great opportunity for our people.”
Mr Vardkar said he hoped the deal would lead to a “positive outcome for Ireland”.
“It is a once-in the-a.d. time in the history of the EU,” he said.
EU leaders are set to meet in Brussels, Belgium, on Tuesday for talks on a new agreement to end decades of acrimony over Ireland’s refusal to join the bloc.
The UK and France have been demanding Ireland accept the single market and the EU’s customs union.
Mr Varady said the EU needed to do more to address the “unprecedented challenges” facing the island, which is one of the poorest countries in Europe.
“We need to take our foot off the gas and let the people of Ireland know what we’re doing here,” he told reporters.
“I hope the EU will take this opportunity to make progress and be a great partner in Ireland.”
Mr Cameron has said he is “very pleased” with the progress made.
“The agreement reached in Brussels will have to be approved by the European Parliament and the European Council, which will then need to ratify it,” he tweeted.
“There is more to do but it is time to get on with it.”
Mr Davids Government has pledged to bring forward the timetable for the agreement and has said it is looking to the European Commission to negotiate the deal over the next few months.
It said it has “zero tolerance” for “the continued delays and delays to the implementation of the agreement”.