Rehnquist, 80, died Saturday evening after a battle with thyroid cancer and after serving more than 33 years on the nation's highest court -- nearly 19 as the chief justice.
In remembering the chief justice of the United States, President Bush praised Rehnquist as a man of conscience and a thoughtful scholar in American history and law.
"We remember the integrity and the sense of duty that he brought to every task before him," President Bush said, according to the Associated Press. He also stressed the steady, guiding presence the chief justice brought to the court.
Justice Sandra Day O'Connor, who attended law school with Rehnquist more a half-century ago, eulogized her colleague as an insightful, witty and persuasive leader.
"He was clearly the brightest student in our class," she said.
But she equally praised the manner in which he led the court, saying, "He never twisted arms to get votes," but, instead, relied on the power of his arguments.
Bush administration officials and Washington dignitaries filled the historic Catholic Church of St. Matthew's Cathedral for the funeral, where President Kennedy's funeral was held in 1963 and Pope John Paul II celebrated Mass in 1979.
Although Lutheran, Rehnquist's family requested the use of the church because it offered more room than other locations.
Washington, D.C., Cardinal Theodore McCarrick, who welcomed the assembled, praised Rehnquist as a "loving father and husband, an outstanding legal scholar, a tireless champion of life and a true lover of the law: in every sense, a great American."
Rehnquist laid in repose in the Supreme Court building Tuesday and Wednesday and hundreds filed past the jurist to pay their last respects.
Officials, colleagues and former law clerks came forward to offer words of praise and remembrance of the man so many simply called "the chief."
"He kept the members of the court together, despite their many differences," said Sen. George Voinovich, R-Ohio, according to the Associated Press.
Sen. Pete Domenici, R-N.M., called Rehnquist "a great intellect who matured tremendously" during his more than three decades of service on the Supreme Court.
"You have someone who is widely praised as an administrator and chief, who's been fair and equitable with all the justices and managed to win their respect and regard" -- despite often sharp differences of opinion, Shirley Abrahamson, chief justice of the Wisconsin Supreme Court in Rehnquist's home state, told the Washington Post. "He stood up for administrative issues and judicial independence."
One former law clerk told the AP that Rehnquist would likely be bemused by the national and international attention his passing attracted.
"In some ways, he may be looking down at all of this, and be amused by it all; he was a person who liked being anonymous," said Joseph Hoffmann, a former Rehnquist clerk who teaches law at Indiana University.
Officials at Arlington National Cemetery listed the chief justice as "William Rehnquist, Sgt., USA," signifying the rank he attained while serving in the U.S. Army during World War II. His burial plot lies alongside his wife who died in 1991 and is in an older section of the cemetery, not far from where former Chief Justice Warren Burger and Justices Harry Blackmun, William Brennan, William Douglas, Potter Stewart and Thurgood Marshall are buried, reported the AP.