"In a world moving toward liberty, we are determined to show the meaning and promise of liberty," the nation's 43rd president said in hisoutside the U.S. Capitol.
The oath was administered by ailing, who is battling thyroid cancer and must breathe through a tracheotomy tube.
It was the fifth time Rehnquist has sworn in a president.
Moments earlier, Vice President Dick Cheney was sworn-in for a second term by House Speaker J. Dennis Hastert of Illinois.
After the ceremony, the president and his family joined congressional leaders and the nation's political elite for lunch at the Capitol, and then left for the traditional inaugural parade.
As is customary, the president and first lady Laura Bush got out of their limousine and walked for a few blocks along the parade route, waving and acknowledging cheers from the crowd.
Up to half a million people lined Pennsylvania Avenue amidfor the chance to glimpse Mr. Bush's motorcade.
Miles of metal barricades gave a fortress-like feel to the city, which is well acquainted with post-Sept. 11 safety measures.
Three of President Bush's predecessors joined him on the platform at his inauguration. Former President Carter, his wife, Rosalynn; former President Clinton and Sen. Hillary Rodham Clinton, D-N.Y; and Mr. Bush's parents, former President George H.W. Bush and Barbara Bush, attended the ceremony.
Former President Ford, who is 91 and no longer travels extensively, did not attend. He lives in California.
In his inaugural address, Mr. Bush offered an implied rebuttal to critics of his foreign policy and the war in Iraq – without actually mentioning the conflict that has claimed the lives of more than 1,300 Americans and was a key fault line in last fall's election.
"Some, I know, have questioned the global appeal of liberty," he said, "though this time in history, four decades defined by the swiftest advance of freedom ever seen, is an odd time for doubt."
"We go forward with complete confidence in the eventual triumph of freedom," he said.
Mr. Bush's 21-minute speech referred unmistakably to the 9-11 attack and the events that have followed.
"We are led, by events and common sense, to one conclusion. The survival of liberty in our land increasingly depends on the success of liberty in other lands," he said.
"The best hope for peace in our world is the expansion of freedom in all the world."
Mr. Bush said he would place the nation on the side of the world's oppressed people.
"Our country has accepted obligations that are difficult to fulfill and would be dishonorable to abandon," he said.
"All who live in tyranny and hopelessness can know: the United States will not ignore your oppression, or excuse your oppressors. When you stand for your liberty, we will stand with you."
The inaugural address went through 21 drafts as of Wednesday afternoon and was timed at 17 minutes. The address was intended to be inspirational, with Mr. Bush'sleft to be spelled out in his State of the Union speech on Feb. 2.
The president's main speechwriter, Michael Gerson, told CBS News Correspondent Bill Plante that Mr. Bush "very much wanted this to be the freedom speech."
It's "the first inaugural address since 9/11, and those events, and the events that followed, have changed America's approach to the world," Gerson said.
Mr. Bush's victory in November made him the 16th president in American history to win a second full term – an accomplishment denied his father, George H.W. Bush in 1992. In the process, he led Republicans to larger majorities in the House and Senate, and has outlined a conservative second-term domestic agenda that includes major changes in Social Security and taxes.
But with the war in Iraq a major concern – and worries over terrorism, the future of Social Security, the high cost of health care and a slow job market – Mr. Bush begins his new term with the lowest approval rating of any recent president to win re-election: 49 percent inreleased Wednesday.
Not everybody was cheering four more years of the Bush presidency.
Democrats did little to hide their disappointment. "Personally, I don't feel much like celebrating. So I'm going to mark the occasion by pledging to do everything in my power to fight the extremist Republican's destructive agenda," House Democratic Leader Nancy Pelosi wrote in a fundraising appeal for 2006.
There were smallat scattered locations, including one several miles from the Capitol where anti-war protesters carried coffin-like cardboard boxes to signify the death of U.S. troops in Iraq.
A small group of protesters close to the inaugural stands tried to interrupt Mr. Bush's speech, but he ignored their chants.
For all the security precautions, officials reported no new information suggesting terror threats to the ceremony or the parade that was following.