British Prime Minister Theresa May says an agreement between Britain and the European Union guarantees the rights of 3 million EU citizens in the UK and 1 million Britons elsewhere in the bloc.
She also says it ensures there will be no hard border between Northern Ireland and the Republic of Ireland after Brexit.
She says Northern Ireland has "a set of unique circumstances" because it has the UK's only land border with an EU country.
The border issue has been threatening to derail the divorce talks.
Earlier this week, a Northern Ireland party that propped up May's government scuttled a deal between the UK and the bloc, prompting frantic diplomacy.
May said Friday that the agreement would maintain an open border while preserving the constitutional and economic integrity of the UK.
European Commission President Jean-Claude Juncker is lauding the breakthrough in Brexit talks and says he will recommend that negotiations be broadened to future relations and trade.
Juncker told reporters Friday that "I believe that we have now made the breakthrough that we needed."
He said that he would recommend to European Union leaders that "sufficient progress has been achieved" on the terms of the divorce to starting talking about issues like future relations and trade.
EU leaders meet in Brussels next Thursday and are likely to endorse the assessment that enough progress has been made on the terms of Britain's financial settlement, the status of Irish borders and the rights of citizens hit by Brexit.
Chancellor Philip Hammond congratulated UK Prime Minister Theresa May on Twitter: "Delighted a deal agreed in Brussels that paves way for further progress on talks about future UK/EU relationship. A positive step.
"Today's announcement in Brussels is a boost for Britain's economy. Now let's conclude a trade deal that supports Britain's jobs, businesses and prosperity."
The European Union's chief Brexit negotiator Michel Barnier tweeted a video of a sprinter jumping hurdles with the caption: "First #Brexit hurdles taken ... more to come."
The chairman of European Union leaders, Donald Tusk: "We are ready to start preparing a close UK-EU partnership in trade but also fight against terrorism and international crime, as well as security, defence and foreign policy."
Ireland's foreign minister said.Simon Coveney told broadcaster RTE: "What it means is any deal that is done has to be better than the default position, otherwise we won't be able to agree it.
"I think what that does is, it puts a floor under what is possible in terms of the outcome that we can't fall below, so Ireland obviously has a huge interest in the phase two negotiations."
Ex-Ukip leader Nigel Farage said on Twitter: "A deal in Brussels is good news for Mrs May as we can now move on to the next stage of humiliation."
Scottish First Minister Nicola Sturgeon tweeted: "Move to phase 2 of talks good - but devil is in the detail and things now get really tough.
"If #Brexit is happening (wish it wasn't) staying in single market & customs union is only sensible option. And any special arrangements for NI must be available to other UK nations."
Dr Adam Marshall, director general of the British Chambers of Commerce , said: "Businesses will be breathing a sigh of relief that 'sufficient progress' has been achieved.
After the noise and political brinksmanship of recent days, news of a breakthrough in the negotiations will be warmly welcomed by companies across the UK."