"Another barrier has been broken in American life," said Joe Lieberman, an independent who voted for Sotomayor, the daughter of Puerto Rican parents who moved to New York when she was a child.
The vote in the senate went largely along party lines. Democrats said that Sotomayor had proved that she was even-handed in her application of the law but Republicans accused her of cherry-picking from legal precedents in order to pursue a political agenda.
Sotomayor's critics had pointed to comments that a "wise Latina" woman might reach a better decision than a white man as evidence that she was biased.
At her confirmation hearing, Sotomayor said that her comments could have been phrased differently but insisted that she had always maintained fidelity to the law.
Sotomayor is considered to have a liberal outlook similar to Souter, meaning that the court’s ideological balance – five conservatives to four liberals - will remain broadly the same.
Janet Murguia of the National Council of La Raza, a Hispanic civil rights group, said: "This vote will matter - and it will be long remembered."
Hispanics make up 15 per cent of the US population and voted by a two-to-one margin for Obama in the 2008 presidential election.
The supreme court is the final arbiter in US law and rules on issues as diverse as abortion, gun rights, business, the death penalty and civil rights.