Kagan, 50, swore to administer justice evenly to the rich and poor alike and to follow the Constitution.
The audience, including Kagan's family and friends and five justices, erupted in cheers as soon as Chief Justice John Roberts finished administering the oath. Kagan, who supplants Roberts as the court's youngest member, smiled ear-to-ear.
Roberts actually swore in Kagan twice. She recited one oath as prescribed by the Constitution during a private ceremony in a conference room at the court with only her family present.
Roberts then administered a second oath, taken by judges, with Kagan's family and friends, including her brothers Marc and Irving, and reporters present. Also in attendance were Justices Anthony Kennedy, Clarence Thomas, Ruth Bader Ginsburg and Sonia Sotomayor.
The ceremony was nearly identical to the one that took place a year ago for Sotomayor and must have surely pleased the man Kagan replaces, retired Justice John Paul Stevens, who criticized the decision of some justices to be sworn in at the White House. Stevens also was in attendance Saturday.
Kagan won't be formally installed as a justice until Oct. 1 in a courtroom ceremony at the start of the court's new term.
Kagan, who is stepping down as U.S. solicitor general, celebrated her new job with President Obama Friday at the White House in front of an audience filled with Kagan's friends and extended family, along with Justices Ruth Bader Ginsburg and Anthony Kennedy.
"While she may be feeling a twinge of sadness about giving up the title of general -- a cool title -- I think we can agree that Justice Elena Kagan has a pretty nice ring to it," Obama said of his second successful appointment to the court.
Kagan thanked Obama for trusting her enough to nominate her to the Supreme Court and pledged to fulfill an "obligation to uphold the rights and liberties afforded by our remarkable Constitution" and "to provide what the inscription on the Supreme Court building promises: equal justice under law."
Fox News' Lee Ross contributed to this report.