At 50, Kagan, is relatively young for the lifetime post and could help shape the high court's decisions for decades. If confirmed by the Senate, she would become only the fourth female justice in history.
Obama cited what he called Kagan's "openness to a broad array of viewpoints" and her "fair mindedness."
Standing beside the president in the East Room of the White House, Kagan said she was "honored and humbled by this nomination."
"I look forward to working with the Senate in the next stage of this process, and I thank you again, Mr. President, for this honor of a lifetime," she said.
Republicans are expected to criticize her for attempting to bar military recruiters from the Harvard Law campus while she was dean. That issue was used against her by critics during her confirmation hearing last year for her current post.
With control of 59 votes in the Senate, Democrats should be able to win confirmation. However, if all 41 Republicans vote together, they could delay a vote with a filibuster.
Republicans have shown no signs in advance that they would try to prevent a vote on Kagan, but they are certain to grill her in confirmation hearings over her experience, her thin record of legal writings and her decisions at Harvard.
The senator who will preside over her confirmation hearing, Democrat Patrick Leahy of Vermont, said, "The Senate should confirm Ms. Kagan before" Labor Day.
"Our constituents deserve a civil and thoughtful debate on this nomination, followed by an up-or-down vote," said the chairman of the Senate Judiciary Committee.
The Republican Senate leader, Mitch McConnell of Kentucky, said his party would make sure there was a "thorough process, not a rush to judgment" on the nomination.
"Judges must not be a rubber stamp for any administration. Judges must not walk into court with a preconceived idea of who should win," he said, adding that Republicans would have a vigorous debate on that principle.
Obama introduced Kagan as "my friend."
"Elena is widely regarded as one of the nation's foremost legal minds. She's an acclaimed legal scholar with a rich understanding of constitutional law. She is a former White House aide, with a life- long commitment to public service and a firm grasp of the nexus and boundaries between our three branches of government," Obama said.
Kagan served in the Clinton White House.
Obama began with high praise for the retiring Stevens, a leader of the court's liberals, calling him "a giant in the law," impartial and having respect for legal precedence.
Kagan "embodies the same excellence, independence and passion for the law," Obama said.
He noted that neither Kagan's mother nor father "lived to see this day, but I think her mother would relish this moment. I think she would relish, as I do, the prospect of three women taking their seat on the nation's highest court for the first time in history ... a court that would be more inclusive, more representative, more reflective of us as a people than ever before."
Kagan praised Stevens for having "played a particularly distinguished and exemplary role. It is therefore a special honor to be nominated to fill his seat."
In a short tenure as solicitor general "I have felt blessed to represent the United States before the Supreme Court, to walk into the highest court in this country when it is deciding its most important cases, cases that have an impact on so many people's lives," she said.
Seven Republicans voted for her confirmation last year as solicitor general.
One of them, Orrin Hatch of Utah, a member of the Judiciary Committee, issued a statement saying his decision this time "will be based on evidence, not blind faith. Her previous confirmation and my support for her in that position do not by themselves establish either her qualifications for the Supreme Court or my obligation to support her."
Kagan would become the only justice who had no prior experience as a judge. The other justices all served previously as federal appeals court judges. She was nominated to a federal appeals court post by President Bill Clinton but never served.
That means Kagan has a smaller paper trail than other recent nominees since there are no prior decisions to scrutinize.
But conservatives were already mounting an attack, one they laid the groundwork for when she was mentioned last year as being on Obama's short list for the Supreme Court post last time around.
Obama's White House team was launching its own broad campaign-style outreach to Capitol Hill and the media. That effort is designed to shape the national image of Kagan, an unknown figure to much of America.
Her selection came after nearly a monthlong process of consideration. Obama always had Kagan on his short list but still considered a broader group of candidates, interviewing four.
The president informed Kagan that she would a Supreme Court nominee on Sunday night. He then called the three federal judges he did not choose for the position, Diane Wood, Merrick Garland and Sidney Thomas.
Kagan is known as sharp and politically savvy and has enjoyed a blazing legal career. She was the first female dean of Harvard Law School, first woman to serve as the top Supreme Court lawyer for any administration.
A source close to the selection process said a central element in Obama's choice was Kagan's reputation for bringing together people of competing views and earning their respect.
The seven Republicans who supported her when she was confirmed as solicitor general in 2009 included Hatch, Tom Coburn of Oklahoma, Susan Collins of Maine, Judd Gregg of New Hampshire, Jon Kyl of Arizona, Richard Lugar of Indiana and Olympia Snowe of Maine.
Kagan has clerked for Thurgood Marshall, worked for Bill Clinton and earned a stellar reputation as a student, teacher and manager of the elite academic world. Yet she would be the first justice without judicial experience in almost 40 years. The last two were William H. Rehnquist and Lewis F. Powell Jr., both of whom joined the court in 1972.
Supreme Court justices wield enormous power over the daily life of Americans. Any one of them can cast the deciding vote on matters of life and death, individual freedoms and government power. Presidents serve four-year terms; justices have tenure for life.
Democrats went 15 years without a Supreme Court appointment until Obama chose federal appellate judge Sonia Sotomayor last year to succeed retiring Justice David Souter. Just 16 months in office, Obama has a second opportunity with Kagan.
Kagan, who is unmarried, was born in New York City. She holds a bachelor's degree from Princeton, a master's degree from Oxford and a law degree from Harvard.
Before she served as a clerk for Justice Marshall, she clerked for federal Appeals Court Judge Abner Mikva, who later became an important political mentor to Obama in Chicago.
Kagan and Obama both taught at the University of Chicago Law School in the early 1990s.
In her current job, Kagan represents the U.S. government and defends acts of Congress before the Supreme Court and decides when to appeal lower court rulings.
Texas Senator John Cornyn reacts to Supreme Court Nominee Cornyn released the following statement in response to the nomination of Kagan
U.S. Sen. John Cornyn (R-Texas), a member of the Senate Judiciary Committee and Republican Leadership, today released the following statement after President Obama's nomination of Solicitor General Elena Kagan to replace Justice John Paul Stevens on the U.S. Supreme Court:
"Now that President Obama has nominated Solicitor General Elena Kagan to replace Justice John Paul Stevens on the U.S. Supreme Court, the Senate must provide its advice and consent. It is essential that the Senate perform this Constitutional duty in a thorough manner and give Ms. Kagan's record a full and fair review.
"There is no doubt that Ms. Kagan possesses a first-rate intellect, but she is a surprising choice from a president who has emphasized the importance of understanding 'how the world works and how ordinary people live.' Ms. Kagan has spent her entire professional career in Harvard Square, Hyde Park, and the DC Beltway. These are not places where one learns 'how ordinary people live.' Ms. Kagan is likewise a surprising choice because she lacks judicial experience. Most Americans believe that prior judicial experience is a necessary credential for a Supreme Court Justice.
"If confirmed as a life-tenured justice, Ms. Kagan's rulings could affect the life, liberty, and property of Americans for generations. So we must learn completely about her judicial philosophy and commitment to our founding principles. And we must ensure that she rejects judicial activism and holds fast to the belief that justice is blind.
"Ms. Kagan failed to answer many questions posed by senators prior to her confirmation as solicitor general. This failure led many members to oppose her nomination. I hope that she will now more willingly respond to reasonable and relevant questions.
"America deserves a nominee who reveres the law and applies it impartially. Through the confirmation process, I look forward to determining whether Ms. Kagan meets this high standard and is fit to serve as an associate justice."
Senator Cornyn serves on the Finance, Judiciary, Agriculture and Budget Committees. He serves as the top Republican on the Judiciary Committee's Immigration, Refugees and Border Security subcommittee. He served previously as Texas Attorney General, Texas Supreme Court Justice, and Bexar County District Judge.