On a hectic day in which the US Congress voted to end a government shutdown, the Senate gave the final nod to Kennedy and 22 other nominees unanimously without roll call votes.
Kennedy, who was days away from her sixth birthday when her father was assassinated 50 years ago next month, will step into the most public role of her adult life after largely shying away from the family profession of politics.
Kennedy had told the hearing that her father, who was seriously wounded by a Japanese destroyer in World War II, had hoped to pay the first US state visit to Tokyo. With his assassination, the trip was not carried out until 1974 when Gerald Ford visited.
"I would be humbled to carry forward his legacy in a small way and represent the powerful bonds that unite our two democratic societies," Kennedy told the committee.
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Kennedy's nomination has been hailed in Japan, although several US experts have voiced concern at having a diplomatic novice in Tokyo at a time of high tensions between the close ally and a rising China.
With her parents and brother all dead, Kennedy has championed her family's brand of progressive politics while generally preferring to stay out of the limelight.
But Kennedy played a pivotal role in her Democratic Party's primary in 2008 when she was an early and vocal backer of Obama against perceived front-runner Hillary Clinton.