The UK and EU have reached agreement on how rules in the Brexit divorce deal will be implemented, particularly in relation to Northern Ireland.
The government says an "agreement in principle" has been found for issues including border control posts and the supply of medicines.
Details of the agreement have not been published but are expected to be rubber stamped in the coming days.
Separate negotiations to reach a post-Brexit trade deal are still ongoing.
The UK left the EU in January but has continued to follow the same rules and regulations during what is known as the transition period.
The new border arrangements will apply regardless of whether the two sides agree a deal to govern their trading relationship after the Brexit transition period ends on 31 December.
Controversial powers withdrawn
The UK government also agreed to withdraw controversial clauses from its Internal Market Bill, which is currently going through parliament.
Ministers had threatened to use the bill to introduce powers which could override parts of the Brexit divorce deal it signed last year - the withdrawal agreement, potentially breaking international law.
It said it wanted a "safety net" to prevent a "border down the Irish Sea" in case talks with the EU broke down.
The threat had risked jeopardising the separate negotiations over a UK-EU trade deal, which are heading into a crucial stage, but the UK has now dropped plans to put the powers into law.
The agreement follows talks in Brussels between Cabinet Office Minister Michael Gove and EU commissioner Maroš Šefčovič, which have taken place alongside the negotiations over a new trade agreement.
Speaking after the announcement, Mr Gove said he was "delighted" and thanked the EU team for their "constructive and pragmatic approach".
Brexit - The basics
- Brexit happened but rules didn't change at once: The UK left the European Union on 31 January 2020, but leaders needed time to negotiate a deal for life afterwards - they got 11 months.
- Talks are happening: The UK and the EU have until 31 December 2020 to agree a trade deal as well as other things, such as fishing rights.
- If there is no deal: Border checks and taxes will be introduced for goods travelling between the UK and the EU. But deal or no deal, we will still see changes.
'Stability and security'
Mr Gove told reporters: "We've agreed stability and security for Northern Ireland", adding: "We will be able to ensure unfettered access for goods which come from Northern Ireland to the UK" and "given certainty to businesses in Northern Ireland".
He said there "will be some necessary checks on food and products of animal origin as they go into Northern Ireland" but added these are checks that reflect the fact that the island of Ireland has always been treated as a single zone for animal health.
Mr Gove added "there will be a small number of precautionary checks on food products when they go into Northern Ireland" but emphasised they would be "as light touch as possible".
He said businesses in Northern Ireland would have the access to the "best of both worlds" access to the single market without infrastructure and at the same time "unfettered access to the rest of the UK market".
'Big obstacle' removed
Mr Šefčovič said the agreement had removed "one big obstacle" from the trade talks, and would create "positive momentum" for the negotiators.
Speaking to reporters in Brussels, he added that the negotiating teams are "still very far apart, and we are not hiding this from anyone".
Welcoming the news, Irish Foreign Affairs Minister Simon Coveney told RTE News the new border deal was a "very important positive for the island of Ireland".
"It's hopefully a signal that the British government is in a deal-making mood and we can carry some momentum from this," he added.
Northern Ireland's First Minister Arlene Foster said her Democrat Unionist Party would await details of the new agreement before passing judgement.
She added it was important any new arrangements ensure Northern Irish businesses can trade freely with firms in Great Britain.
The pledge from UK ministers to remove the powers comes just one day after they ordered Conservative MPs to reinstate them to the bill on Monday. They had been removed from the bill by the House of Lords.
This is a Brexit breakthrough.
But not on those three sticking points we've heard so much about in the last few days: fishing rights, competition rules and enforcing any agreement.
You may remember all of the rows over the last few years about the border on the island of Ireland: how do you keep it open, with Northern Ireland outside of the European Union, and the Republic within it?
That is what this is about: working out mutually acceptable rules that will keep Northern Ireland more closely aligned to the EU than the rest of the UK.
What has happened today is a necessary, but far from sufficient, step as the two sides attempt to reach a free trade deal.
But one thing it unquestionably does is improve relations between the two sides - with the UK no longer threatening to breach the last deal it did with Brussels, the withdrawal agreement, at just the point it's trying to sort out the next one.
The Brexit withdrawal agreement - or divorce deal - sets out the details of the UK's exit from the EU, which took place earlier this year.
Northern Ireland is the only land border between the UK and the EU.
Under an arrangement known as the Northern Ireland protocol - which is part of the withdrawal agreement - from January, goods will not need to be checked along the Irish border and the region will continue to enforce the EU's customs product standards rules.
This means, in order to comply with EU requirements, some checks will be needed on certain goods entering Northern Ireland from Great Britain (England, Scotland and Wales).
In September, the EU expressed anger when the UK government published its Internal Market Bill, which would have enabled ministers to ignore some of the Northern Ireland protocol requirements.
For example, it would have allowed ministers to override sections of the Brexit divorce deal specifying that companies moving goods from Northern Ireland to Great Britain would have to fill out export declaration forms.
Efforts to reach a UK-EU trade deal remain stalled over disagreements on fishing rights, business competition rules and how any deal would be enforced.
Boris Johnson - who is due to travel to Brussels on Wednesday in a bid to break the deadlock - has described the situation as "very tricky" but added that "hope springs eternal".