The former dean of Harvard Law School joined two other women on the nine-member court, including Sonia Sotomayor, the first Hispanic supreme court justice, who was nominated by Obama and confirmed by the senate last year.
Kagan, 50, had served for just over a year as the solicitor-general for Barack Obama, the US president, arguing US government cases before the supreme court, when he nominated her in May.
She replaces former justice John Paul Stevens, who retired in June, two months after turning 90.
Kagan is also the first justice in four decades to reach the supreme court without ever having served as a judge.
The Senate vote on Thursday fell mostly along party lines, with five Republicans and two independents joining 56 Democrats in supporting Kagan.
One Democrat, Ben Nelson of the state of Nebraska, voted against approving her.
Republicans painted Kagan as an enemy of gun rights and of curbs on abortion, and denounced her for setting limits on military recruitment at Harvard because of her disapproval of the "Don't Ask, Don't Tell" ban on gays serving openly.
Kagan's service in the administration of Bill Clinton, the former US president, also created concern amongst Republicans.
"Americans expect politics to end at the courtroom door," Mitch McConnell, the Republican leader in the senate, said.
"Nothing in Elena Kagan's record suggests that her politics will stop there."