She would also be the 112th and youngest member of the court, and the appointment would mean that there are three female justices on the court for the first time.
Kagan, who is close to Obama, was the first female dean of Harvard Law School, the first woman to be the most senior supreme court lawyer, and worked as deputy assistant for domestic policy to Bill Clinton, the former president.
She has said in the past that she would uphold the constitutionality of laws that say that states do not need to recognise same-sex mariages in other states. With regard to abortion, she has said that she will respect current laws and precedent.
As the Harvard Law School dean, Kagan openly railed against the military's "don't ask, don't tell" policy regarding homosexual service members.
She called it discriminatory and barred military recruiters over the matter until the move threatened to cost the university federal money.
When Kagan was confirmed as solicitor general she agreed with a questioner that if a person was believed to be assisting al-Qaeda financially, he or she should be subject to battlefield law, including detention without trial, even if the suspect was captured in a non-conflict zone.
Some of Kagan's liberal criticshave seized on that case, and others, to warn that Kagan might make the court more conservative.
Her defenders, like Harvard University law professor Lawrence Lessig, point out that the solicitor general is required to defend a particular position - and that her past work might not illustrate her political views.
"The [solicitor general] is not philosopher in chief. She is not hired to decide what laws she likes and dislikes," Lessig wrotein a Huffington Post essay last month. "Her job is to defend the government so long as a defense is constitutionally plausible."
"A plausible defense is plainly different from one's own view of the law."
Pushing for greater consensus
The nine-member supreme court has extensive power over American life, with a single justice able to vote decisively on individual freedoms, government power and matters of life and death.
The president's power to nominate supreme court justices is one of the most important roles that presidents have.
Obama has said that he wants greater consensus among the members of the court and Kagan is someone who can potentially lead greater unity having apparently cultivated ties with some conservatives.
The seat on the supreme court was made available by the retirement justice John Paul Stevens.