He will lie in repose in the Great Hall of the Supreme Court on Tuesday and Wednesday.
The public will be able to pay its respects Tuesday from 10:30 a.m. until 10 p.m. Eastern time, and on Wednesday from 10 a-m Eastern time until noon.
Rehnquist, who died yesterday at age 80, will be buried Wednesday at Arlington National Cemetery, where his wife was laid to rest in 1991.
Justice John Paul Stevens, the court's senior justice, will fill the administrative role of chief justice until a new one is confirmed.
Stevens repeatedly clashed with Rehnquist over court rulings, but today called him "an inspiration to those of us privileged to serve with him."
Rehnquist, who oversaw the high court's conservative shift and presided over the impeachment trial of President Clinton, had spent 33 years on the Supreme Court.
Rehnquist's death opens a rare second vacancy on the nation's highest court and gives President Bush, whose election Rehnquist helped decide, an opportunity shape the makeup of the court for years to come.
The president on Sunday called Rehnquist a man of "character and dedication" and said he would work swiftly to fill the two openings at the Supreme Court.
"It will serve the best interest of the nation to fill those vacancies promptly," Bush said in a brief message in the Roosevelt Room of the White House.
"I will choose in a timely manner a highly qualified nominee to succeed Chief Justice Rehnquist," Bush said.
"The Chief Justice battled thyroid cancer since being diagnosed last October and continued to perform his duties on the court until a precipitous decline in his health the last couple of days," court spokeswoman Kathy Arberg said in announcing his death.
Rehnquist was surrounded by his three children when he died at his home in suburban Arlington, Va.
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.
The death leaves Bush with his second court opening within four months and sets up what's expected to be an even more bruising Senate confirmation battle than that of John Roberts.
It was not immediately clear what impact Rehnquist's death would have on confirmation hearings for Roberts, scheduled to begin Tuesday. There is some talk that the hearing could be postponed because of memorial services for the chief justice.
The last time there were simultaneous vacancies at the court was 1971, when Justices Hugo Black and John Marshall Harlan retired in September, about a week apart. Rehnquist, then a Justice Department lawyer, urged the Nixon administration to move fast in replacing them and wound up being appointed to Harlan's seat himself.
Rehnquist presided over 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 deeply 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.
Many court watchers had expected the ailing chief justice 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. 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.
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