Sotomayor, 54, would be the first Hispanic on the high court if confirmed. She would succeed Justice David Souter, who is retiring.
The president, in his announcement, said he was looking for a justice with a "common touch and a sense of compassion" as well as experience and depth of knowledge. He said Sotomayor, who grew up in a Bronx housing project and has an extensive judicial background, would come to the Supreme Court bench with more varied experience than anyone currently on the court when they were appointed.
Sotomayor, who said she was "deeply moved" by the president's decision, called herself an "ordinary person who has been blessed with extraordinary opportunities and experiences."
Obama called Sotomayor an "inspiring woman who I believe will be a great justice."
"Judge Sotomayor has worked at almost every level of our judicial system, providing her with a depth of experience and breadth of perspective that will be invaluable as a Supreme Court justice," Obama said.
Sotomayor's selection indicates that Obama is interested in diversifying the court. If she is confirmed, Sotomayor will become the third woman to be a Supreme Court justice, and she will join Ruth Bader Ginsburg in the current court.
Obama had said he was looking for a nominee who demonstrates empathy and "intellectual fire power," as well as possesses the "common touch." The president on Tuesday described Sotomayor, a judge for the 2nd Circuit Court of Appeals, as someone who fits these criteria.
She is the daughter of Puerto Rican parents, and she was raised in a Bronx housing project. She has dealt with diabetes since age 8 and lost her father at age 9, growing up under the care of her mother. Sotomayor supposedly became interested in law after watching the TV show "Perry Mason."
She graduated from Princeton University and earned her law degree from Yale University. Sotomayor was appointed a federal district court judge in 1992 by President George H.W. Bush and then elevated to the 2nd Circuit Court of Appeals by President Bill Clinton. At that time, Republicans held up her confirmation, but she eventually passed the Senate 68-28.
Tuesday's selection drew swift praise from liberals like the Rev. Al Sharpton, who called the choice "prudent" and "groundbreaking." New York Sens. Chuck Schumer and Kirsten Gillibrand, Democrats from Sotomayor's home state, also praised the pick and released a letter they wrote to Obama earlier in the month recommending her as an "excellent selection."
Souter generally sided with the liberal wing of the high court, so Obama's selection would not tilt the ideological balance of the body. But Sotomayor was considered one of the most liberal of Obama's potential nominees, and she could set off a fight from the right during confirmation -- even though Republicans are far outnumbered on Capitol Hill.
"This is not a bipartisan, consensus pick," one senior GOP Senate leadership aide told FOX News.
As an appellate judge, she sided with the city of New Haven, Conn., in a discrimination case brought by white firefighters after the city threw out results of a promotion exam because two few minorities scored high enough. Ironically, that case is now before the Supreme Court.
A YouTube video of Sotomayor speaking at Duke University about what some interpreted as judicial activism also stirred controversy.
In the video, she said: "All of the legal defense funds out there, they're looking for people with court of appeals experience" because "the court of appeals is where policy is made."
Obama's nomination is the first by a Democratic president in 15 years.
His announcement also gives the Senate four months -- more than enough by traditional standards -- to complete confirmation proceedings before the Court begins its next term in the fall.
Republicans have issued conflicting signals about their intentions. While some have threatened filibusters if they deemed Obama's pick too liberal, others have said that is unlikely.
"Senate Republicans will treat Judge Sotomayor fairly," Senate Republican Leader Mitch McConnell said in a written statement. "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 even-handedly, despite their own feelings or personal or political preferences."
The announcement comes after the president met with his legal team Monday at the White House to discuss the selection. He also read through written material on potential picks over the weekend at Camp David, according to a White House official who spoke on the condition of anonymity.
The president had kept a tight lid on the identity of the nominee. The presumptive short list included several women, including Sotomayor and another Appeals Court judge, Diane Wood.
Senior officials said Obama interviewed Sotomayor, Kagan, Wood and Napolitano, deciding Monday on Sotomayor. Obama notified her Monday night of his decision.
"He was very interested in her from the start," a senior official said.
FOX News' Major Garrett, Lee Ross and Trish Turner and The Associated Press contributed to this report.