Kan is the country's fifth prime minister since 2006. The Diet, Japan's parliament, voted after the Democratic Party of Japan tapped Kan to lead the party earlier Friday.
"The very first thing we must do is to regain the trust of the people," Kan said in a speech to party members before their vote Friday.
Kan promised transparent government and pledged improved policies to boost jobs and reinvigorate society.
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"I have confidence that economic growth and social welfare can be realized together," he said.
In the lower house of the Diet, Kan garnered 313 out of 480 votes Friday. In the upper house, he won by a narrower margin, getting 123 of 242 votes.
In addition to serving as finance minister in the Hatoyama administration, Kan served as deputy prime minister.
But Kan will be a rare political breed for a Japanese premier: His family has not produced another prime minister or state minister, which could play well with a Japanese public that has seen several sons and grandsons of former ministers in the past year ascending to the premiership only to step down again a few months later.
As a former health minister, Kan gained popularity with voters after exposing a government cover-up of HIV-tainted blood products that caused thousands of hemophilia patients to contract the virus that causes AIDS.
As a state minister for economy, he was not shy to talk about the foreign currency exchange rate. In January, he was supportive of a weaker yen to help the export-driven Japanese economy.
Eight months ago, Hatoyama 's Democratic Party of Japan won a sweeping victory, an outcome hailed by many as a revolution in Japanese politics. With promises of a cleaner government, Hatoyama worked to shift the political dynamics in Japan by taking away power from the bureaucrats and granting more power to politicians and local governments.
But allegations of illegal campaign financing soon tarnished his administration's image. Some of his cabinet members were investigated for corruption.
His approval rating took further hits over his failed promise to move a major U.S. Marine base off Okinawa to ease the burden of the island, which hosts the majority of the United States military presence in Japan. Earlier this month, calling his decision "heartbreaking," he announced that the base would remain on Okinawa, although relocated to a different part of the island.
Hatoyama's critics claimed he gave in to U.S. pressure, and his government coalition broke up.