The government consists, apart from the Social Democratic Party, of the liberal Vidreisn (approximately Renewal) and the populist Folkpartiet.
The government has as its goal to reduce interest rates and inflation, and wants to hold a referendum on potential citizenship in the EU.
Frostadóttir, 36, becomes the country's youngest prime minister, according to the Icelandic public service company Rúv.
She is also the world's youngest currently sitting prime minister, according to Rúv.
It is the first time Iceland has a government where there are more women than men, and where all party leaders are women. It is also the first time the country has both a female president – Halla Tómasdóttir – and a female prime minister.
