The Prime Minister confirmed that MPs would get a vote on the new “Windsor Framework” at an “appropriate time”.
”Together we have changed the original protocol and are today announcing the new Windsor Framework,” he said.
“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 deal was a “decisive breakthrough" on post-Brexit trading arrangements.
Ms von der Leyen, who arrived in London on the Eurostar this morning, added that the agreement was “historic”.
“We knew it was not going to be easy,” she said.
“We knew we needed to listen to each other's concerns very carefully. Above all, we had to listen to the concerns of the people of Northern Ireland. We knew we had to work hard with clear minds and determination.”
Mr Sunak did not confirm when MPs would get to vote on the deal in the Commons.
“Parliament will have a vote at the appropriate time and that vote will be respected,” he said.
“I think it's important that we give everyone the time and the space they need to consider the detail of the framework that we've announced today because it is comprehensive in nature and that will take time for people to digest.”
Mr Sunak won strong backing from senior Tories to defy the Democratic Unionist Party and hardline Eurosceptic MPs if they seek to torpedo his new protocol arrangements.
They stated that this was a moment to show “leadership” and to make “big calls” under pressure.
They urged him to “go for it” and to “get on with the reforms” to ease tensions with the European Union, boost ties with the United States and restore powersharing in Northern Ireland.
The deal introduces a new system of green and red lanes for goods travelling from Britain to Northern Ireland, stripping back paperwork and checks for good that will remain in the province.
But it also means Northern Ireland continuing to have to follow new single market laws, with the European Court of Justice also having an ongoing role.
Hardline Tory Eurosceptics were voicing deep concern over the plan on Monday morning, but it was expected to win the backing of the vast majority of MPs.
Former Cabinet minister Sir Robert Buckland told Sky News: “Taking some risks, making difficult decisions, grasping nettles is a really important part of what it is to be a leader. The Prime Minister is demonstrating that at the moment.”
He added: “I very much hope that he succeeds. It will be a demonstration of his resolution and his ability to under big pressure make those big calls.”
Sir Robert Syms, former Tory party vice-chairman, said: “Rishi is showing leadership. He is being cautious because he wants to bring as many people with him, which is a sensible approach. But nobody has a veto on this.”
Ex-Cabinet minister Jacob Rees-Mogg, though, signalled a possible Tory revolt if the Democratic Unionist Party does not support the deal, despite the major concessions by Brussels, including giving ground on tax, state aid and Stormont’s say on new laws coming from Brussels.
He told GB News: “If the DUP are against it, I think there will be quite a significant number of Conservatives who are unhappy.”
He emphasised that the position of Boris Johnson, who led the Brexit campaign, would be “fundamental”.
The King was due to hold an audience with Ms von der Leyen at Windsor Castle later on Monday afternoon.
A palace spokesman said: “The King is pleased to meet any world leader if they are visiting Britain and it is the Government’s advice that he should do so.”
Mr Rees-Mogg stressed that it would be a mistake for Ms von der Leyen to meet the King before MPs approve the deal.
Former Cabinet minister Sir John Redwood added: “The main issue in EU talks is not the occasional intervention of the European Court but the continuous imposition of European law on a part of the UK.”
The DUP and European Research Group were expected to examine the fine detail of the deal before coming to a firm position on whether to oppose or support it.
But other senior Tories urged Mr Sunak not to allow Brexit “ultras” to scupper his plans. Former Cabinet minister Sir David Lidington, chairman of the Conservative European Forum, said: “If the Prime Minister’s judgment is that he has got the best deal he can for the national interest of the UK, then he should go for it.”
Sir Charles Walker, a former Conservative Party vice chairman, added: “We must not let perfection be the enemy of the good. That is recognised now by the overwhelming majority of Conservative MPs.”
Tobias Ellwood, Tory chairman of the Commons defence committee, urged MPs to continue supporting Mr Sunak as their party “regroups” following the chaos of the brief Liz Truss premiership.
He said: “Governments get re-elected when they get policy across the line, work for the national interest and exhibit the high standards of statecraft that allows our country to punch above its weight. Governments don’t get re-elected when they look divided, distracted and failing to put the nation’s interests first. The choice is simple.”
The protocol, which was signed by Mr Johnson as premier in 2020, was designed to prevent a hard border with Ireland after Brexit. But it effectively created a border down the Irish Sea between mainland Britain and Northern Ireland, angering Unionists.
The DUP collapsed powersharing in Stormont last year in protest at its impact, leaving Northern Ireland without an executive or an assembly. DUP leader Sir Jeffrey Donaldson, who is seen as less hardline than other leading members of his party, has issued seven tests that Mr Sunak’s new pact will have to meet in order to win the party’s backing.
Chief among them is addressing what he calls the “democratic deficit” of Northern Ireland being subject to EU rules while not having a say on them.
DUP chief whip Sammy Wilson told Talk TV: “We are not going to collaborate in the destruction of the Union. The protocol was breaking us away from it.”
Some hardline Eurosceptics have urged Mr Sunak to keep the threat of unilaterally tearing up the protocol, through the Protocol Bill, to maximise pressure on Brussels to give ground. Meanwhile, the Conservative European Forum was today launching an inquiry to identify enterprise-led, practical improvements to the Brexit Trade and Co-operation Agreement.