The agreement came into force in February when the UK left the EU, but the Northern Ireland protocol is set to be enacted on January 1 2021, when the transition period ends and the UK leaves the single market and customs union.
But on Tuesday, Mr Gove and Mr Sefcovic confirmed they would withdraw the most controversial aspects of the bill.
The pair co-chair the EU-UK Joint Committee which oversees the implementations of the Withdrawal Agreement. Their discussions are separate from the ongoing struggles to secure a post-Brexit trade deal by the end-of-year deadline.
In a joint statement, the two sides said: “Following intensive and constructive work over the past weeks by the EU and the UK, the two co-chairs can now announce their agreement in principle on all issues, in particular with regard to the Protocol on Ireland and Northern Ireland.”
In view of these “mutually-agreed solutions”, the Government will ditch clauses 44, 45 and 47 of the UK Internal Market Bill – which could have overridden the divorce deal Britain agreed with the bloc last year.
The Government has also pledged not to introduce any similar provisions in the Taxation Bill which is due to come before MPs in the House of Commons later on Tuesday.
The agreement covers issues including border checks on animal and plant products, the supply of medicines and deliveries of chilled meats and other food products to supermarkets.
There was also “clarification” on the application of rules on state subsidies.
Mr Gove shared his joy at the development on Twitter, writing: “Delighted to announce agreement in principle on all issues in the UK-EU Withdrawal Agreement Joint Committee.
“Thank you to @MarosSefcovic and his team for their constructive and pragmatic approach.”
He said he would update Parliament on Wednesday.
The breakthrough comes as Boris Johnson warned that trade talks were proving “very tricky” ahead of a crunch meeting with Brussels’ top official.
The Prime Minister said he was still hopeful about reaching a deal but it was proving “very, very difficult” to make progress.
Later this week Mr Johnson will head to Brussels for face-to-face talks with European Commission chief Ursula von der Leyen in an attempt to salvage a deal, with time running out before the current trading arrangements expire at the end of the month.
Mr Johnson said he hoped the “power of sweet reason” would triumph but Brussels had to accept there were limits to what terms the UK would be prepared to accept.
Negotaitions have faltered on the issues of fishing rights, the “level playing field” measures aimed at preventing the UK undercutting the EU on standards and state subsidies, and the way that any deal would be governed.
In a message to Brussels, the PM said: “Our friends have just got to understand the UK has left the EU in order to be able to exercise democratic control over the way we do things.
“There is also the issue of fisheries where we are a long way apart still.
“But hope springs eternal, I will do my best to sort it out if we can.”
Boris Johnson ‘hopeful’ for Brexit trade deal but admits situation is ‘very tricky’
Mr Johnson’s trip to Brussels is seen as a make-or-break moment for the process after months of talks led by Lord Frost and the EU’s Michel Barnier.
Downing Street said Lord Frost would return to London later on Tuesday to discuss the remaining differences in reaching a free trade deal with Mr Johnson.
Then “over the course of the coming days” the Prime Minister will go to Brussels, Number 10 said, though no meetings are planned with the leaders of either France or Germany.
“There are just limits beyond which no sensible, independent government or country could go and people have got to understand that.”
He again insisted the UK will “prosper mightily” with or without a trade deal with the EU despite grim warnings from the budget watchdog and the governor of the Bank of England about the impact.
The Office for Budget Responsibility has suggested that a no-deal situation could wipe two per cent off gross domestic product – a measure of the size of the economy, in 2021.
Bank governor Andrew Bailey has warned that the long-term damage caused by a no-deal situation would be worse than the economic hit from coronavirus.
But Mr Johnson urged people to “be in good cheer” as there were “great options ahead” for the country.
Germany’s European affairs minister, Michael Roth, said “political will in London” was needed to get a deal.
“Let me be very clear, our future relationship is based on trust and confidence,” he said.
“It’s precisely this confidence that is at stake in our negotiations right now. We want to reach a deal, but not at any price.”
No day has yet been fixed for Mr Johnson’s meeting with Mrs von der Leyen, but it is expected later this week and follows a lengthy telephone call on Monday.