National has been negotiating with the right-wing libertarian ACT party and populist NZ First party since the last month's election.
The support of the two minor parties is crucial for National to secure a parliamentary majority and be able to form a government.
On Monday, Mr Luxon told journalists outside Auckland's Cordis Hotel he had finalised individual deals with the two parties.
"We have actually closed out and agreed our policy programs with both ACT and also with New Zealand First. That's a major achievement," he said.
The parties are working towards a first in NZ politics: a formal three-way coalition government with cabinet representation from all three parties.
Mr Luxon said the talks had taken more than a month as the parties went "line by line" through their various policy pledges and party manifestos.
On many policies, there is alignment between the three, but on others, they have clashed and made concessions.
"All three parties have had to make trade offs along the way. That will be revealed when we make our final announcements," Mr Luxon said.
The parties have also had to overlook campaign hostilities.
Both Mr Luxon and ACT leader David Seymour argued vociferously against voting for Winston Peters' NZ First party during the election.
When final results showed Mr Peters' party would be needed to form a majority government, both reluctantly accepted the need to work with 78-year-old veteran.
"We've brought together three who have been competitors, sometimes fierce competitors, at the election," Mr Seymour told breakfast television show AM.
"Fierce competitors during the election, constructive cooperators in a cabinet. That's quite a transition."
Speaking after the announcement, Mr Peters showed the awkward transition in effect when he told reporters it was "an assumption" a policy deal had been done.
It was not clear whether Mr Peters was signalling discomfort with his deal, or sticking to a pact with other leaders to keep their discussions confidential.
At this point, ACT and NZ First will compare their deals and flag any final issues before a deal can be done.
Mr Luxon said the parties had been keeping each other in the loop in recent weeks, which means he didn't anticipate major issues.
The former Air New Zealand chief executive, who declared himself "very relieved" to have the policy discussions done, was so confident he said he was moving onto ministerial allocations.
"Now today, we want to kick on and move on into ministerial responsibilities and cabinet positions," he said.
"I don't think that needs to take a long time. We're going to work very quickly through it as fast as we possibly can.
"There is very good intention from from all three party leaders to resolve this as quickly as possible."
Mr Luxon also acknowledged growing impatience among Kiwis for a deal to be done, with the talks taking longer than any post-election negotiations since 1996.
"I really do appreciate everybody's patience with the process but I do believe it'll actually make for a much stronger government," he said.
"That's what these three parties are going to deliver.
"We are in this together. And it's important that we can actually support each other's policy."
As of Monday, it has been 37 days since the October 14 election, with the outgoing Labour administration functioning as a caretaker government since then.
National won 38.1 per cent of the vote at the election, compared with ACT on 8.6 per cent and NZ First on 6.1.
Translated into seats in parliament, National will have 48 MPs, ACT will have 11 and NZ First eight, combining for 67 MPs.
Either National or NZ First's caucus will grow by one after the Port Waikato by-election on Saturday, which confirms the make-up of the 123-seat parliament.
