A statement from the spokeswoman said he was surrounded by his three children when he died in Arlington.
"The Chief Justice battled thyroid cancer since being diagnosed last October and continued to perform his dues on the court until a precipitous decline in his health the last couple of days," she said.
CBS News Correspondent Howard Arenstein reports that in mid-July, Rehnquist issued a statement quashing rumors he would retire saying "I will continue to perform my duties as chief justice as long as my health permits."
Rehnquist appeared weak and frail in public, Arenstein adds. At least twice over the last two months he was admitted to a hospital with a fever
Rehnquist was appointed to the Supreme Court as an associate justice in 1971 by President Nixon and took his seat on Jan. 7, 1972. He was elevated to chief justice by President Reagan in 1986.
His death ends a remarkable 33-year Supreme Court career during which Rehnquist oversaw the court's conservative shift, presided over an impeachment trial and helped decide a presidential election.
The death of the chief justice now gives President Bush his second chance in four months to put someone on the high bench Arenstein reports.to learn more about possible nominees for chief justice.
The death sets up what's expected to be an even more bruising Senate confirmation battle than that of John Roberts.
According to areleased roughly the same time as Rehnquist's pledge to stay on the bench, Americans are split on whether the Senate should examine a nominee's positions on specific issues.
Forty-five percent think the Senate should consider only the nominee's legal qualifications and background, while 47 percent think the Senate should also consider how the nominee might vote on major issues the Supreme Court decides.
It was not immediately clear what impact Rehnquist's death would have on confirmation hearings for Roberts, scheduled to begin Tuesday.
Rehnquist presided over President Clinton's impeachment trial in 1999, helped settle the 2000 presidential election in Bush's favor, and fashioned decisions over the years that diluted the powers of the federal government while strengthening those of the states.
Arberg said plans regarding funeral arrangements would be forthcoming.
Bush was notified of Rehnquist's death shortly before 11 p.m. EDT.
"President Bush and Mrs. Bush are saddened by the news," said White House counselor Dan Bartlett. "It's a tremendous loss for our nation." The president was expected to make a personal statement about Rehnquist on Sunday.
The chief justice passed up a chance to step down over the summer, which would have given the Senate a chance to confirm his successor while the court was out of session, and instead Justice Sandra Day O'Connor announced her retirement to spend time with her ill husband. Bush chose Roberts, a former Rehnquist clerk and friend, to replace O'Connor.