EU and UK negotiators have reached a draft agreement on a new Brexit deal before a meeting of European leaders in Brussels.
The prime minister tweeted: "We've got a great new deal that takes back control - now parliament should get Brexit done on Saturday so we can move on to other priorities like the cost of living, the NHS, violent crime and our environment."
Leaders are now expected to give their political approval to the revised withdrawal agreement and political declaration on Thursday afternoon.
The draft agreement addresses how to avoid a hard border on the island of Ireland after Brexit, tackling issues such as customs controls and consent for the Northern Ireland Assembly.
The DUP has cast doubt on its success, saying they still cannot support it.
Labour leader Jeremy Corbyn said the deal sounded "even worse" than what was negotiated by the PM's predecessor, Theresa May, and "should be rejected" by MPs.
But European Commission President Jean-Claude Juncker said it was a "fair and balanced agreement".
In a letter to the president of the European council, Donald Tusk, Juncker said it was time for the British House of Commons to do its part to bring the first phase of the negotiations to an end.
He wrote: "I believe it is high time to complete the withdrawal process and move on, as swiftly as possible, to the negotiation on the European Union's future partnership with the United Kingdom."
Both he and Johnson have urged their respective parliaments to back the deal.
The EU's chief negotiator Michel Barnier told a press conference in Brussels: "We have arrived at an agreement with the British government on an ordered withdrawal of the United Kingdom and the
European Union and also on the framework for our future relationship."He added that the text should provide "the legal certainty in every area where Brexit, like any separation, creates uncertainty and in particular, and first and foremost, for citizens".
Key points from a draft version of the new Brexit agreement include the consent mechanism for Northern Ireland. This ensures that the Democratic Unionist party cannot veto the new customs and regulatory rules as they will not have a simple majority in Stormont, the seat of the Northern Ireland assembly.
Johnson is reported to have ditched his "two borders" proposals and will instead accept the six counties will remain in a customs union with Brussels in all but name.
The EU, meanwhile, has agreed for Northern Ireland - in what would be a complex dual-tariff arrangement - to be allowed to officially remain in a customs territory with the UK, meaning the region can benefit from trade deals inked by the Government and any lower tariffs agreed by ministers.
The arrangement would keep the Irish internal border open but create checks in the Irish Sea on goods travelling between Northern Ireland and Great Britain, a situation that crosses the DUP's "blood red" line.
However, without DUP backing, there remains little hope that the deal will pass through the British parliament.
Xavier Bettel, prime minister of Luxembourg, said: "I'm the one who always wanted to have a deal. No deal is bad for all of us. So a deal is good."
Mark Rutte, the Dutch prime minister, said: "We have to study the details but in itself [it is] very encouraging," pointing to a stack of papers in his hand. He refused to say whether or not his country would back the proposed deal at this stage.
The Commons will sit on Saturday, the first weekend sitting in 37 years, to discuss the proposal following the EU summit in Brussels. The government will put forward the new agreement for a vote, which has the support of the cabinet.
Sterling fell 0.5% to $1.2762 after the DUP statement, but news of a deal from the prime minister sent it back up 1%, to $1.29 dollars, a five-month high. It was up 0.5% against the Euro.
Nigel Green, the CEO and founder of deVere Group, said:
The pound has soared above $1.29 for the first time since May on reports that a Brexit deal has been reached and UK stocks are boosted in a relief rally.
"However, the rally is currently being tempered as it needs to get through the UK and EU parliaments.
"There does seem to be some question marks remaining over the DUP's support, which is, of course, critical to getting the deal through the House of Commons.
"That said, there does seem to be a growing sense of optimism that it can get approved."
He continues: "If this deal is ratified, we can expect the pound to jump sharply. It is likely to hit at least $1.35 as the prospect of a no-deal, and/or months of further uncertainty ends.
"Sentiment towards UK stocks will also rally, particularly given the attractive valuations of many UK companies.
"However a strong pound may dilute the impact on exporters, as their earnings in dollars and euros, amongst others, will become less valuable in sterling terms."
The deVere CEO concludes: "There is potential for a significant relief rally for the pound and UK financial assets if this new Brexit deal is approved.
"However, even if it is passed, this is really just the beginning - not the end.
"As such, investors need to protect themselves from market uncertainty and also best-position themselves for the inevitable opportunities through exposure to a broad range of assets, currencies and geographic regions."