Sandra Day O'Connor, the first woman to serve on the US Supreme Court and a crucial centrist, is to retire.
Justice O'Connor has regularly cast the deciding vote
Ms O'Connor, 75, has often cast the deciding vote on the nine-member court, leading some US commentators to call her the most powerful woman in America.
She is the first Supreme Court justice to retire since 1994, giving George W Bush his first chance to name a judge.
The former Arizona politician was nominated by Ronald Reagan to serve on the court and took up her seat in 1981.
In a statement at the White House, President Bush praised Ms O'Connor as a "discerning and diligent judge", who has earned universal respect.
He said he would consult with senators to find a successor, and said he would be "deliberate and thorough" in his search.
The president's nomination to the court must be approved by the Senate.
Speculation has mounted that Mr Bush will now nominate a conservative to the court in an effort to tilt the balance of opinion on the bench.
The president called for a "dignified process", which he aims to conclude by the start of the new Supreme Court term in early October.
Despite originally joining the justices as a conservative, Ms O'Connor became a centrist who regularly voted for both liberal and conservative measures.
Her stance on critical issues such as abortion, which she views neither as unconstitutional nor as an unquestionable human right, has often guided the court.
Ms O'Connor saw her appointment as a breakthrough for women
The BBC's Justin Webb in Washington says a more reliable conservative could give the court a harder edge on social issues, which would affect the nature of American society for decades.
In a three-sentence letter of resignation to Mr Bush, Ms O'Connor described her 24-term tenure on the court as "a great privilege".
"This is to inform you of my decision to retire from my position as an associate justice of the Supreme Court of the United States, effective upon the nomination and confirmation of my successor," she wrote.
"I will leave it with enormous respect for the integrity of the court and its role under our constitutional structure."
Ruth Bader Ginsburg is currently the only other woman sitting on the bench.
Liberal and conservative interest groups have been preparing for battle over the appointment of a new justice for many years.
There had been speculation that Chief Justice William Rehnquist, 80, who is suffering from thyroid cancer, would be the first judge to retire.
The departure of Ms O'Connor, whose vote was often crucial, is expected to add greater urgency to the nomination debate.
Senator John McCain, a potential Republic candidate to succeed Mr Bush as president, said of Ms O'Connor: "She did make history."
"I am confident that President Bush will appoint a Supreme Court justice who shares his philosophy, which is a conservative philosophy," Mr McCain told CNN.
According to reports, both camps have amassed record sums to spend on adverts promoting or attacking candidates for the vacancy.
Brian McCabe, president of the conservative pressure group Progress for America, said Mr Bush's choice "deserves genuine consideration - not instant attacks".
Ralph Neas, of the liberal organisation People for the American Way, described the nomination process as "a crucial test" for Mr Bush.