Sebastian Kurz, 27, was one of 12 ministers confirmed by Austrian President Heinz Fischer in the capital Vienna.
Before taking up his new role, Sebastian Kurz was state secretary for integration.
Austria’s ruling bloc, the Social Democrats and the conservative People’s Party, won the election in September.
The Social Democrats came top with 27.1%, while the People’s Party got 23.8%.
Seen as a rising star in the People’s Party, Sebastian Kurz had earned praise in his previous post for his work in schools and with Muslim immigrants.
As secretary, he followed a policy of integrating immigrants into Austrian society by requiring their children to speak German before entering school.
Sebastian Kurz also established free language classes for Muslim religious leaders and launched a forum for dialogue with Islam.
Although the ruling parties have won another five-year term in a coalition, last month’s election was their worst result since World War II.
A series of scandals and perceived inertia have hit the parties’ popularity among the voters.
The anti-immigration and Eurosceptic Freedom Party appears to have benefited from this slump, reaping 21.4% of the vote.
The party has accused the coalition of bloating the public sector, corruption and permitting too much immigration.
Other people in positions of power around the world include Kim Jong-un, who became leader of North Korea at the age of 28 or 29 (his exact age is not known).
Roosevelt Skerrit was 32 years old when he became prime minister of Dominica in 2004.
Jigme Khesar Namgyel Wangchuck is one of the youngest monarchs in the world. He became king of Bhutan in 2008 at the age of 28.
Swaziland’s King Mswati III was 18 when he was crowned in 1986.
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