Kagan, 50, the former dean of Harvard Law School, pledged to "do equal right to the poor and to the rich" as she took the second of two required oaths from Chief Justice John Roberts, who congratulated her and welcomed her to the court.
"We look forward to serving with you in our common calling," Roberts said after administering the oath. A formal investiture will take place on Oct. 1, three days before the justices begin their next term.
The U.S. Senate voted 63-37 to approve her appointment by President Barack Obama after a summer of debate over the role of judges and the sharply divided court under Roberts. Only five Republicans supported her; one Democrat, Ben Nelson of Nebraska, opposed her.
Kagan succeeds Justice John Paul Stevens, who retired after 35 years. She is likely to take his place as one of the four justices who take more liberal positions on such issues as abortion, gun rights and campaign finance.
A New York native, Kagan is the first woman to be U.S. solicitor general, representing the Obama administration before the Supreme Court. She worked for four years in President Bill Clinton's White House as a lawyer and policy adviser. She served as dean of Harvard Law School from 2003 to 2009, and in the late 1980s was a law clerk to Supreme Court Justice Thurgood Marshall.
Kagan's stint as solicitor general will probably prevent her from taking part in some Supreme Court cases early in her tenure.
Tom Goldstein, a Washington appellate lawyer whose Scotusblog website tracks the court, estimated that she may have to disqualify herself from 13 cases in her first term and five in the following one because of the role her office has played in pending litigation.
Ronald Rotunda, a professor at Chapman University School of Law in Orange, California, said at Kagan's Senate confirmation hearings that she should disqualify herself in any case in which she gave advice on the merits of a dispute. That would include instances in which the Obama administration asked her opinion on the constitutionality of proposed legislation, he testified.
Kagan is likely to excuse herself from the first case to be argued when the justices take the bench on Oct. 4. The dispute involves minimum prison sentences and Kagan signed a legal brief opposing high court review.
Kagan said during the confirmation process that she would decide on a case-by-case basis whether to recuse herself from considering challenges to the new federal overhaul of health care.
Marshall was the last solicitor general to ascend to the court and disqualified himself in more than 60 argued cases in his first term.
Today's televised swearing-in reflected a change in venue that Obama urged to stress the independence of the court system. Starting with Sandra Day O'Connor in 1981, each new justice took the oath at the White House until last year when the ceremony for Sotomayor returned to the stately marble building where the Supreme Court has met since its construction 75 years ago.
Before Sotomayor, Stevens in 1975 was the last justice to take the oath away from the White House. Stevens said last year that holding the ceremony at the White House was "incorrect symbolism."