Ms Sotomayor, 55, becomes only the third woman to sit on the court.
On Thursday, the Senate voted 68-31 to approve her with 59 Democrats and nine Republicans voting in favour.
The Supreme Court is the highest court in the US, with the power to strike down unconstitutional laws. Once appointed, justices serve for life.
They are nominated by the president, but must receive approval from a majority of senators before they can take up their post.
Ms Sotomayor was sworn in by Chief Justice John Roberts at a brief ceremony that was the first one open to television cameras in the court's history.
Standing next to her mother and brother, she pledged to "faithfully and impartially" discharge her duties.
The public ceremony followed a private one minutes earlier in which she promised to support and defend the constitution.
Sonia Sotomayor is President Barack Obama's first nominee to the nine-member court.
Her appointment - as a successor to liberal Justice David Souter, who retired - is not expected to change its ideological balance.
Ms Sotomayor was born to poor Puerto Rican parents on a New York public housing project, rising to become a respected judicial scholar and judge.
Some Republicans had been critical of her record of speeches - and some rulings - saying they had revealed that she allowed her opinion to affect her decisions.
During her confirmation hearing before the Senate Judiciary Committee, she was asked repeatedly about a speech in which she had remarked that "a wise Latina woman with the richness of her experiences would, more often than not, reach a better conclusion" than a white male judge.
Critics said the remark could have been perceived as racist, but Ms Sotomayor maintained the comments had been an attempted "play on words" that "fell flat".