"In a world moving toward liberty, we are determined to show the meaning and promise of liberty," the nation's 43rd president said in hisat the noontime ceremony at the U.S. Capitol.
Mr. Bush made a sweeping pledge to spread liberty and freedom "to the darkest corners of the world."
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.
Earlier, Vice President Dick Cheney was sworn-in for a second term by House Speaker J. Dennis Hastert of Illinois.
A crowd of more than 100,000 people gathered in snowy Washington for the swearing-in at the West Front of the Capitol and the traditional parade down Pennsylvania Avenue.
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 plan to attend. He lives in California.
Snipers were dispatched to rooftops and bomb-sniffing dogs into the streets, amidfor the inauguration ceremonies. Miles of metal barricades gave a fortress-like feel to the city, which is well acquainted with post-Sept. 11 safety measures.
Mr. Bush, 58, awoke before dawn Thursday in the White House and then traveled by motorcade with his wife Laura and their twin daughters, Jenna and Barbara, to nearby St. John's Church for the traditional pre-inauguration prayer service.
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.
Inaugurations, though, are a time to talk about hope.
"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," said the president in his speech.
"The best hope for peace in our world is the expansion of freedom in all the world," he continued.
The inaugural address went through 21 drafts as of Wednesday afternoon and was timed at 17 minutes. The address is 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.
Elaborating on this point, first lady Laura Bush told Plante, "We saw millions of people line up to vote in Afghanistan and over 40 percent of that number of people that voted were women, who had been totally excluded from civic life a mere three years ago. We have a vote coming up in Iraq. We see people who are suffering the threat of violence but are still determined to vote."
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.
Some Bush opponents took vacations to get away from the inaugural hoopla while others flocked to Washington to give the president a symbolic snub. They plan to turn their backs on the president as his motorcade rolls down Pennsylvania Avenue.
A myriad of other protests are planned for Inauguration Day, including: a march with coffins and a die-in (protestors lying down en masse in the streets) in opposition to the Iraq war; a rally in favor of nominating Supreme Court justices opposed to abortion; and a rally by HillaryNow.com in protest of what the group calls "the Coronation of Bush" and in support of Senator Clinton for president in 2008.
There will also be numerous "counter-inaugural" balls for Bush opponents.
The protests will be "nothing compared to the late 1960s and early 1970s, and other times in American history where the protests have been intense," Larry Sabato, a professor at the Center of Politics of the University of Virginia, told Early Show co-anchor Rene Syler.