Both are considered to be "liberal" justices and the appointment is unlikely to change the ideological balance of the court, which shifted to the right under the Bush administration.
Divorced with no children and reputed to be a "workaholic", Sotomayor has often spoken of the courts as being "the last refuge for the oppressed".
She is a federal district judge from New York who grew up in the poor Bronx part of the city. Her parents are from Puerto Rico.
"I strive never to forget the real world consequences of my decisions on individuals, businesses and government,'' she said on Tuesday.
Republicans have said that they will scrutinise Sotomayor's views on the importance of personal experiences in shaping legal rulings, which conservatives oppose in favour of a strict reading of the law.
"She must prove her commitment to impartially deciding cases based on the law, rather than based on her own personal politics, feelings, and preferences," said John Cornyn, a Republican senator.
Susan Karamanian, an associate dean at George Washington University law school in Washington DC, told Al Jazeera the appointment showed he wanted "somebody who is well-established in the law, that has a variety of experiences".
"Somebody who is prepared to perhaps take a little more, if there are some of these cases where there’s judgement room, to perhaps look at fairness factors, to perhaps look at the experience of the underdog and the like."
Justices serve until they retire or die, giving presidents an opportunity to influence policy long after their terms end.
The supreme court is one of the three branches of the US government, the final court of appeals and the final arbiter of the US constitution.