The United Kingdom and the European Union have sealed a deal to resolve their thorny post-Brexit trade dispute over Northern Ireland, hailing the agreement as the start of a “new chapter” in their often fractious relationship.

Prime Minister Sunak and the European Commission president, Ursula von der Leyen, announced the grandly titled “Windsor Framework” after agreeing to the final details at Windsor, near London.

Ms. Von der Leyen said during a news conference Monday it was “historic what we have achieved today.” Mr. Sunak said there had been a “decisive breakthrough.”

The agreement, which will allow goods to flow freely to Northern Ireland from the rest of the U.K., ends a dispute that has soured U.K.-EU relations, sparked the collapse of the Belfast-based regional government, and shaken Northern Ireland’s decades-old peace process.

Fixing it ends a long-running irritant for Ms. von der Leyen and is a big victory for Mr. Sunak — but not the end of his troubles. Selling the deal to his own Conservative Party and its Northern Irish allies may be a tougher struggle. Now Sunak awaits the judgment of Northern Ireland’s Democratic Unionist Party, which is boycotting the region’s power-sharing government until the trade arrangements are changed to its satisfaction.

Northern Ireland is the only part of the United Kingdom that shares a border with an EU member, the Republic of Ireland. When the U.K. left the bloc in 2020, the two sides agreed to keep the Irish border free of customs posts and other checks because an open border is a key pillar of Northern Ireland’s peace process.

Instead, there are checks on some goods entering Northern Ireland from the rest of the U.K. That angered British unionist politicians at Belfast, who say the new trade border in the Irish Sea undermines Northern Ireland’s place in the United Kingdom.

The Democratic Unionist Party collapsed Northern Ireland’s Protestant-Catholic power-sharing government a year ago in protest and has refused to return until the rules are scrapped or substantially rewritten.

The party’s leader, Jeffrey Donaldson, said there had been “significant progress” but “key issues of concern” remained. He said the party would study the details before responding.

The devil, as ever, will be in those details, and the two sides emphasized different elements of the deal.

According to the new plan, goods will be split into two different trading lanes.

Mr. Sunak said the new rules “removed any sense of a border in the Irish Sea” by eliminating checks and paperwork for the vast majority of goods entering Northern Ireland. Only those destined to travel onward to EU member Ireland will be checked.

He said Northern Ireland’s lawmakers would be able to block any changes to EU goods laws that applied to them by using an emergency mechanism labeled the “Stormont Brake” after the home of the Northern Ireland Assembly.

“Today’s agreement delivers smooth-flowing trade within the whole United Kingdom, protects Northern Ireland’s place in our union, and safeguards sovereignty for the people of Northern Ireland,” Mr. Sunak said.

The role of the European court in resolving any disputes that arise over the rules has been the thorniest issue in the talks. London and Brussels agreed in their Brexit divorce deal to give the European court that authority. Yet the DUP and Conservative Party euroskeptics insist the court must have no jurisdiction in British matters.

The British pound rose against the dollar after the deal was announced, and business groups welcomed the agreement. The head of the Confederation of British Industry, Tony Danker, said it would “allow businesses and politicians to turn their attention to economic growth and delivering greater prosperity.”

Now Mr. Sunak will have to face down his Conservative critics — including Prime Minister Johnson, who as leader at the time signed off on the trade rules that he now derides. Mr. Johnson was ousted by the Conservatives last year over ethics scandals, but is widely believed to hope for a comeback.

In a boost for Mr. Sunak’s chances of winning Conservative support, lawmaker Steve Baker — a self-styled “Brexit hardman” who helped topple Prime Minister May by opposing her Brexit deal in 2019 — said he was “delighted” with the agreement.

Mr. Sunak said lawmakers in Parliament would get a vote on the deal “at the appropriate time,” but not right away.

Even if Mr. Sunak faces a rocky road at home, the deal likely marks a dramatic improvement in relations with the EU. They were tested severely during the long Brexit divorce and chilled still further amid disputes over the Northern Ireland Protocol.

Under Mr. Johnson, the British government introduced a bill that would let it unilaterally rip up parts of the Brexit agreement, a move the EU called illegal. Mr. Sunak’s government said the bill would now be dropped.