"This is a wonderful day for Judge Sotomayor and her family, but I also think it's a wonderful day for America."
With his fellow Democrats holding a majority in the Senate, Mr Obama was not expected to face any difficulties getting his nominee confirmed.
In advance of the Senate vote, a number of moderate Republicans indicated that they would also be backing her, making her confirmation even more likely.
Ms Sotomayor's supporters say she has a reliable record - and they cite her "inspiring" life story.
She was born to poor Puerto Rican parents on a New York public housing project, rising to become a respected judicial scholar and judge.
But some Republicans claim Ms Sotomayer's record of speeches - and some rulings - shows she allows 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".
Ms Sotomayor has also been criticised by conservatives for upholding a ruling in June last year, rejecting the reverse discrimination claims of white firefighters in Connecticut.
The Supreme Court later ruled in favour of the white firefighters.
Because she is replacing a retiring liberal justice - David Souter - correspondents say Ms Sotomayor is unlikely to alter the current political balance of the court.
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