Obama said Sotomayor has more experience as a judge than any current member of the high court had when nominated, adding she has earned the "respect of colleagues on the bench," the admiration of lawyers who appear in her court and "the adoration of her clerks."
"My heart today is bursting with gratitude," Sotomayor said from the White House podium moments after being introduced by Obama.
If confirmed by the Senate, she would join Justice Ruth Bader Ginsburg as the second woman on the current court, the third in history. She would succeed retiring Justice David Souter.
Obama and Sotomayor both noted the historic nature of the appointment. The president said a Hispanic on the court would mark another step toward the goal of "equal justice under law."
Sotomayor, 54, said she grew up in poor surroundings and never dreamed she would one day be nominated for the highest court.
Obama has said he hopes she can take her place before the justices begin their new term in October.
Democrats hold a large majority in the Senate, and barring the unexpected, Sotomayor's confirmation should be assured.
The Senate Republican leader, Sen. Mitch McConnell of Kentucky, issued a statement that said: "Senate Republicans will treat Judge Sotomayor fairly. But we will thoroughly examine her record to ensure she understands that the role of a jurist in our democracy is to apply the law evenhandedly, despite their own feelings or personal or political preferences."