Johnson pulled off a major coup in agreeing a new divorce deal with the European Union leader, paving the way for him to deliver his promise to leave the bloc on October 31.
But Thursday's deal must still pass the House of Commons, which is meeting for a special session on Saturday to debate the text -- and many MPs are strongly opposed.
Looking tired after days of intense negotiations, Johnson told a Brussels press conference late Thursday that he was "very confident" of getting the deal through.
But he has no majority among MPs, opposition parties have come out against the deal and even his parliamentary allies, Northern Ireland's Democratic Unionist Party (DUP), say they cannot support the terms.
If the Commons rejects the deal on Saturday, Johnson will be forced by law to ask the EU to delay Brexit, for what would be the third time -- something he says he will not do.
European Commission President Jean-Claude Juncker sought to focus MPs' minds, saying Brussels can see no need to prolong the tortuous, three-year Brexit process.
"We have a deal, and this deal means there is no need for any kind of prolongation," he said -- although the decision to delay, if requested by London, would be for EU leaders.
He further warned that if British PMs rejected the deal it would create an "extremely complicated situation".
'This is our chance'
Johnson, a leading Brexit campaigner in the 2016 EU referendum campaign, took office in July vowing to keep to the October 31 Brexit deadline, deal or no deal.
He pledged to renegotiate the most contentious elements of a divorce text agreed with Brussels last year, which was rejected by MPs three times.
But he has found that extricating Britain from four decades of economic, legal and political integration with its European neighbours is no easy task.
A compromise deal was finally struck on Thursday, with a new arrangement for keeping open the border between British Northern Ireland and EU member Ireland.
"It looks like we are very close to the final stretch," EU Council President Donald Tusk said after the bloc's leaders endorsed the text.
Johnson has assured his European counterparts that he can get the deal through parliament.
"I'm very confident that when my colleagues in parliament study this agreement, that they will want to vote for it on Saturday, and then in succeeding days," he told reporters.
"This is our chance in the UK as democrats to get Brexit done, and come out on October 31."
But the DUP has said it cannot support the plans, as efforts to avoid checks on the Irish land border would lead to new trade barriers between Northern Ireland and mainland Britain.
The main opposition Labour, Scottish National and Liberal Democrat parties are also against.
Their response sent the pound sinking again after it had earlier risen to five-month peaks on news of the deal.
Boris Johnson held meetings with the DUP and other MPs this week to try to win support for his deal, made calls throughout the day on Thursday and will continue this on Friday, a Downing Street official said.
But with the numbers extremely tight, he needs to win over Labour MPs representing Brexit-supporting seats.
The Labour leadership objects to the new deal because it paves the way for looser ties between Britain and the EU than were previously envisaged, and the party has called for a second referendum on any deal.
"The deal he's proposed is heading Britain in the direction of a deregulated society and a sell-off of national assets to American corporations," Labour leader Jeremy Corbyn said.
But Boris Johnson insisted Britain was committed to the "highest possible standards" for environmental and social protection.
An official said he would seek to reassure individual Labour MPs that these could be guaranteed in a law implementing the Brexit deal, which could be introduced as soon as Monday if parliament backs the agreement.