Rehnquist, the 16th chief justice of the United States, died on Saturday evening at his home in Arlington, Virginia, surrounded by his three children, the court said in a statement.
He was first diagnosed with cancer in October, but had kept working up to the final days of his life.
The news was delivered to President George Bush late on Saturday night, the White House said.
"The president and Mrs Bush are deeply saddened at the passing of Chief Justice Rehnquist," spokeswoman Jeanie Mamo said. "His family is in their thoughts and prayers."
The president was to make a formal comment on Sunday.
Rehnquist had been in and out of hospital since his condition was diagnosed.
But with rumours about his retirement swirling, Rehnquist moved forcefully to quash them in July, insisting he would not retire and that he intended to "continue to perform my duties as chief justice as long as my health permits".
Rehnquist was first appointed to the Supreme Court in 1971 by President Richard Nixon and took his seat on 7 January 1972.
He was elevated to chief justice by President Ronald Reagan in 1986.
Rehnquist was a strong opponent of abortion, gay rights, gun control and affirmative action for minorities.
A fierce defender of the death penalty, Rehnquist often wrote a divergent opinion when in a minority of one, earning himself the title "Lone Ranger".
Rehnquist was one of two dissenters in the key Roe vs Wade case in 1973 which recognised abortion as a constitutional right.
Rehnquist was known as the 'Lone
Ranger' for his divergent opinions
In 1995, he wrote the majority opinion striking down a federal law ordering a "gun-free zone" around state schools, in a landmark decision preserving the rights of individual states.
In 1999, he presided over the impeachment trial of President Bill Clinton in the Senate over accusations that he lied about his affair with White House intern Monica Lewinsky.
A year later, Rehnquist and four other Republican-nominated justices ordered the end of the presidential election ballot recount in Florida, giving the presidency to George Bush.
Born on 1 October 1924, William Hubbs Rehnquist grew up in Shorewood, in the midwestern state of Wisconsin.
The son of an affluent wholesale paper salesman, he joined the Army Air Corps in 1943 and served in North Africa. Upon his return to the United States, he earned a bachelor's degree and a master's degree in political science from Stanford University in California.
Rehnquist attended Harvard University for a year and earned another master's degree before returning to Stanford to study law. He graduated in 1952 at the top of his class.
The former chief justice is survived by his three children: Janet Rehnquist, James Rehnquist and Nancy Spears as well as his sister, Jean Larin. His wife, Natalie Rehnquist, died in 1991.