Standing alongside European Commission President Ursula von der Leyen at a news conference in Windsor, Sunak said the two sides had agreed to remove "any sense of a border" between Britain and its province - a situation that had angered politicians on both sides.
He immediately won plaudits from business groups who welcomed the easing of trade rules, and an EU promise that it would be willing to allow British scientists to join its vast research programme if Sunak's party accepts the deal.
The agreement marks a high-risk strategy for Sunak just four months after he took office. He is looking to secure improved relations with Brussels - and the United States - without angering the wing of his party most wedded to Brexit.
The deal seeks to resolve the tensions caused by the Northern Ireland protocol, a complex agreement which set the trading rules for the British-ruled region that London agreed before it left the EU but now says are unworkable.
Its success is likely to hinge on whether it convinces the Democratic Unionist Party (DUP) to end its boycott of Northern Ireland's power-sharing arrangements. These were central to the 1998 peace deal known as the Good Friday Agreement which mostly ended three decades of sectarian and political violence in Northern Ireland.
"I'm pleased to report that we have now made a decisive breakthrough," Sunak said of his new "Windsor Framework". "This is the beginning of a new chapter in our relationship."
The issue of Northern Ireland has been one of the most contentious related to Britain's 2020 departure from the European Union. A return to a hard border between the province and Ireland, an EU member, could have jeopardised the peace deal.
But it remains to be seen whether the new terms will go far enough to end the political deadlock in Northern Ireland, where perceptions that the protocol loosened ties with Britain have angered many unionist communities.
Sunak is likely to talk up the fact he has secured a so-called "Stormont brake", which he said would allow Stormont - the regional assembly - to stop any "changes to EU goods rules that would have significant and lasting effects on everyday lives". He said that would give London a veto on new rules.
Von der Leyen said she hoped the brake could be avoided if the two sides consulted each other extensively when introducing new laws and regulatory changes.
DUP leader Jeffrey Donaldson said "significant progress" had been made but they would not be rushed into a decision. Another DUP lawmaker, Ian Paisley, told the BBC it did not go far enough, and more talks were needed.
The European Research Group, which brings together pro-Brexit Conservative lawmakers, will work with lawyers to examine the details before giving a verdict, a process that could take around a week.
David Davis, a former Brexit minister, said Sunak had pulled off a "formidable negotiating success", although there has been speculation in Westminster that Boris Johnson could oppose the deal. A source close to the former prime minister said he was studying and reflecting on the proposal.
If the deal is accepted, the new changes would be phased in over the next few years. A parliamentary vote will take place once all parties have had time to study it.
Victory would strengthen Sunak's hold over his Conservative Party and enable him to move past the thorniest issue on his agenda as he seeks to catch up with the opposition Labour Party, now well ahead in opinion polls, before a national election expected in 2024.
Were he to fail, he would probably face a rebellion from the eurosceptic wing of his party, reviving the deep ideological divisions that have at times paralysed the government since the vote to leave the EU in 2016.
Sunak could have left the stand-off unresolved, but officials in London and Belfast say he has been motivated to act ahead of the 25-year anniversary of the Good Friday Agreement, which could entail a visit from U.S. President Joe Biden.
Biden, who often speaks with pride of his Irish roots, on Monday welcomed the deal and described it as an "essential step" to ensuring that the peace from the Good Friday Agreement was preserved.
U.S. officials had previously warned that any action which endangered the peace agreement could harm the prospects of a U.S.-UK trade deal.
"I appreciate the efforts of the leaders and officials on all sides who worked tirelessly to find a way forward that protects Northern Ireland's place within the UK's internal market as well as the EU's single market, to the benefit of all communities in Northern Ireland," Biden said in a statement.
Sunak is hoping that a successful outcome will improve cooperation with the EU in areas beyond Northern Ireland, including the regulation of financial services and in helping to stem an influx of migrants in small boats across the Channel.
Raoul Ruparel, a one-time special adviser on Europe to former prime minister Theresa May, said the new terms were much better than he had expected.
"It is worth saying the EU has moved massively," he said on Twitter. "Credit where its due. They look to have listened and taken on board concerns of UK, businesses and unionists in NI."