President Obama announced on Tuesday that he will nominate the federal appeals judge Sonia Sotomayor for the Supreme Court, choosing a daughter of Puerto Rican parents raised in a Bronx public housing project to become the nation’s first Hispanic justice.

Judge Sotomayor, who stood next to the president during the announcement, was described by Mr. Obama as “an inspiring woman who I am confident will make a great justice.”

The president said he had made his decision after “deep reflection and careful deliberation,” and he made it clear that the judge’s inspiring personal story was crucial in his decision. Mr. Obama praised his choice as someone possessing “a rigorous intellect, a mastery of the law.”