“We’ve got a great new deal that takes back control,” he said on Twitter just before heading to Brussels for a crucial EU summit.
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.
Northern Ireland’s Democratic Unionist Party (DUP) has cast doubt on its sign off, saying they still cannot support it.
Britain is due to leave the European Union by October 31, with Johnson racing against time to strike a deal to meet that deadline.
Talks between the UK’s Brexit team, led by secretary of state for leaving the EU Stephen Barclay, and the EU negotiators led by Michel Barnier entered a crunch phase on Wednesday to try and thrash out something that the leaders of the 28 EU member-countries can green-light during their two-day summit.
However, differences remain on proposed customs and tax arrangements between EU nation Ireland and UK territory Northern Ireland post-Brexit.