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.
The government says it will now withdraw controversial clauses in the Internal Market Bill.
However negotiations to reach a post-Brexit trade deal are still ongoing.
The details of the agreement have not been published but are expected to be rubber stamped in the coming days.
They will apply regardless of whether the two sides can agree a trade deal.
Cabinet Office minister Michael Gove said he was “delighted” and thanked the European Commission Vice-President Maroš Šefčovič for his teams “constructive and pragmatic approach”.
Irish Foreign Affairs Minister Simon Coveney welcomed the news and expressed the hope that this would “provide some of the positive momentum necessary to instil confidence and trust and allow progress in the wider context of the future relationship negotiations.”
The withdrawal agreement – or divorce deal – sets out the details of the UK’s exit from the EU.
When the UK leaves the transition period on 31 December, Northern Ireland will be 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 – 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).
Over the past year, Mr Gove and Mr Šefčovič had been engaged in talks on how these checks should be implemented.
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, under the Brexit deal, companies moving goods from Northern Ireland to Great Britain would have to fill out export declaration forms, but ministers would have been able to overrule this.
However as the UK and EU have now reached an agreement in principle, these clauses will be removed from the bill.
The government has also promised not to add similar clauses to the Taxation Bill.
Meanwhile, efforts to reach a UK-EU trade deal have 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 this week in a bid to break the deadlock – has described the situation as “very tricky” but added that “hope springs eternal”.