Mr Johnson 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."
The announcement came as the PM was heading for a crunch EU summit in Brussels and follows days of intense negotiations.
The two sides have been working on the legal text of a deal, but it will still need the approval of both the UK and European parliaments.
The deal has already been criticised by the DUP in Northern Ireland.
The DUP has supported the Conservative government in a confidence and supply agreement since the 2017 general election.
But the party has cast doubt on the latest Brexit deal being signed off, saying it could not support the new deal "as things stand".
It is understood the new deal would see Northern Ireland treated differently from the rest of the UK - something the DUP has great concerns about.
DUP leader, Arlene Foster said: "We have been involved in ongoing discussions with the Government.
"As things stand, we could not support what is being suggested on customs and consent issues, and there is a lack of clarity on VAT.
"We will continue to work with the Government to try and get a sensible deal that works for Northern Ireland and protects the economic and constitutional integrity of the United Kingdom."
But European Commission President Jean-Claude Juncker said it was a "fair and balanced agreement".
Both he and Mr Johnson have urged their respective parliaments to back the deal.