At 7:45 a.m., the White House sent out a press release saying:
The President will make an announcement regarding his nomination for the Supreme Court at 10:15AM EDT in the East Room.
... and shortly thereafter, the Associated Press reported that Obama would name Sonia Sotomayor.
From the New York Times:
If confirmed by the Democratic-controlled Senate, Judge Sotomayor, 54, would replace Justice David H. Souter to become the second woman on the court and only the third female justice in the history of the Supreme Court. She also would be the first Hispanic justice to serve on the Supreme Court. [...]
The president reached his decision over the long Memorial Day weekend, aides said, but it was not disclosed until Tuesday morning when he informed his advisers of his choice less than three hours before the announcement was scheduled to take place.
Mr. Obama telephoned Judge Sotomayor at 9 p.m. on Monday, officials said, advising her that she was his choice to fill the Supreme Court vacancy.
In the coming weeks, expect to hear the words "liberal activist" on a daily basis, along with concerns about Sotomayor's temperament, and of course a barrage of criticism about having empathy.
For more biographical information on Sotomayor, see here, and for further discussion on the nomination, see Drdemocrat's diary.