|Katrin Jakobsdottir, Iceland's new PM|
Together the three parties hold 35 seats out of 63 in the Althingi, Iceland's parliament.
Two members of the Leftist-Green Movement are set to vote against the coalition in Thursday's parliamentary approval, technically giving the new government only a single-seat majority.
Katrin Jakobsdottir will become the country's first Green prime minister and the only ruling Green PM in the world, following in the footsteps of former Iceland president Vigdis Finnbogadottir, who became the world's first elected woman president in 1980.
Iceland is ranked top by the World Economic Forum as having the smallest gender gap among 144 countries in the world indexed.
The news will come as a welcome message to over 300 women political leaders from around the world meeting in Iceland this week for an annual summit aimed at promoting gender equality inside and outside of the political sphere.
Jakobsdottir, 41, is a former journalist and served as education minister in Iceland's first left-leaning government which took power after the country's 2008 economic collapse.
In a recent poll 49.5 percent said that they preferred her to become the next prime minister.
Bjarni Benediktsson, chairman of the Independence Party and outgoing prime minister, will become finance and economy minister in the new Icelandic government, a position he held between 2013-2016, before becoming prime minister.
The deal comes four weeks after snap elections were called in October, when a scandal involving PM Benediktsson's father prompted a government ally to drop out of his ruling coalition - after less than a year in government.
Increased taxes on capital gains, maternity and paternity leave, and infrastructure development are among the key issues for the new government.
The Left-Greens want to finance spending by raising taxes on the wealthy, real estate and the powerful fishing industry, while the Independence Party has said it wants to fund new infrastructure by selling state-owned shares in the country's banks.
Iceland was hard hit during the financial crisis when all three of the country's major privately owned commercial banks defaulted in 2008.
Now the Nordic country is experiencing an economic boom driven by record tourist arrivals, leading to shortage of labour and Icelandic workers demanding pay rises.
Note EU-Digest: Iceland is on the right track and can be an example to many other countries,specially when it comes to closing the gender gap around the world.
Read more: Iceland gets first Green prime minister