It will mark the first time the Green party has been in power, after Kurz's alliance with the far-right collapsed in a corruption scandal and triggered elections in September.
Kurz's People's Party (OeVP) and the Greens made gains in election, bringing them together in unlikely negotiations given Kurz's carefully groomed image as a hardliner on immigration.
Both leaders said Sunday major hurdles dividing their parties had already been cleared.
An accord is widely expected to be announced after a last round of talks, which starts at 1700 local time (1600GMT).
- 'Huge stretch' -
Despite progress, observers said new government will face challenges after Kurz's previous rule with the far-right Freedom Party (FPOe) saw a raft of anti-immigration measures passed, sharply dividing Austrians.
"2020 as a political year of change" ran the main online headline of the Kurier daily Wednesday.
Both the OeVP and the Greens will be hard-pressed to show they have not compromised too much on their key principals and campaign promises when they present the joint government programme.
"From his (Kurz's) perspective, it's a huge stretch and it's also a danger that over time he might lose some of the voters he gained from the Freedom Party," analyst Thomas Hofer told AFP.
The Greens will get four ministries, including an enlarged environment ministry that also comprises infrastructure, traffic, energy and technology, a party representative familiar with the negotiations told AFP on Monday.
The OeVP will maintain control of the rest, including the coveted interior ministry -- previously headed by a far-right official and embroiled in scandal -- and the finance portfolio.
Greens chief Kogler, 58, is set to be vice-chancellor.
Greens official Ewa Ernst-Dziedzic told the Standard daily in an interview published Tuesday that compromises were "part of democracy", and that coalition partners would address challenges rather than "feign harmony and sweep difficult topics under the carpet".
- Trend setter? -
Hofer said other European countries, such as Germany, could also see Conservative-Green party coalitions in the future. Sweden, Finland, Lithuania and Luxemburg already have Greens in government.
"Kurz is setting a certain trend maybe ahead of time, and this is certainly something also on the international stage that he would be able to sell," he said.
Hofer described Kogler as a "pragmatist" who had stabilised the Greens taking on the leadership after the party lost all their parliamentary seats in a shock defeat in 2017, largely due to infighting and splits.
A congress of the party's almost 280 delegates must still endorse the coalition agreement, but they are expected to do so.
"It's a historical chance for them," Hofer said.
The far-right FPOe -- previously riding a wave of populist sentiment seen across Europe -- was routed in the polls after the so-called "Ibiza-gate" graft scandal brought down their then-leader and vice-chancellor in May and caused the government to collapse.
In the September polls, the OeVP managed to pick up disenchanted FPOe voters, getting 37.5 percent in total.
The Greens secured 13.9 percent of the vote, their best-ever result, due to the environment replacing immigration as top voter concern in the country of 8.8 million people.
More about: Austria
