Vice President Cheney administered the oath in a brief ceremony in the White House main foyer.
"We've learned that vast oceans no longer protect us from the dangers of a new era. This government has a responsibility to confront the threat of terrorism where it is found," Mr. Bush said in the 10-minute ceremony.
Ridge was confirmed unanimously by the Senate earlier this week. The former Pennsylvania governor has been Mr. Bush's top adviser on domestic security since soon after the Sept. 11 attacks.
The president praised Ridge as a "decisive and clear-thinking executive" and said he's done an "outstanding job."
The department, housed for now at a Washington Navy base, is supposed to get fully organized over the next few months, reports CBS News Correspondent Bob Fuss. Many expect the process to take years.
Roughly 170,000 federal workers from 22 agencies will eventually be joining the Homeland Security Department in the largest reorganization of the federal government since the Defense Department was created in 1947.
Ridge resigned his job as governor in October 2001 to oversee the administration's homeland security operations, a job that until Friday had him working in a small West Wing office in the White House.
Mr. Bush said the new department's birth "begins a vital mission in the defense of our country."
"We're taking the battle to America's enemies," the president said. "We're destructing their networks. We're destroying their camps. We got them on the run. And we're going to keep them on the run."
Democrats have accused the administration of shortchanging funding for some domestic security programs.
"Just as you can't fight the war in Iraq without additional resources, you can't protect our homeland without additional resources," said Sen. Charles Schumer, D-N.Y. "I hope Tom Ridge is able to persuade the president of this obvious fact,"
Ridge's undersecretary will be Asa Hutchinson, head of the Drug Enforcement Administration, who received unanimous Senate approval Thursday. His responsibilities will range from border control to aviation security.
The department will have its own analytical unit to examine intelligence gathered by the CIA, FBI and other agencies to look for clues about terrorist plots. It also will coordinate with 2 million police, firefighters, medical personnel and other first responders around the country.
Congress in November passed legislation to create the department after lengthy debate on such issues as whistle-blower protections, maintaining civil liberties, collective bargaining for department employees and the division of labor with the CIA and FBI, which will remain independent.
For the next five weeks, the department will be in a transitional mode. Many of the agencies being folded into homeland security won't actually fall under its authority until March 1.
With a first-year budget expected at about $33 billion, the department will combine the Secret Service, Coast Guard, Customs Service, Immigration and Naturalization Service, Transportation Security Administration, Federal Emergency Management Agency and other agencies with security-related functions.
Ridge, a decorated Vietnam War veteran, was elected to the House in 1982 from his hometown area of Erie, Pa., and served for 12 years. In 1994, he became Pennsylvania's governor, winning re-election in 1998.
He becomes the 15th member of Mr. Bush's Cabinet, along with the secretaries of the departments of Agriculture, Commerce, Defense, Education, Energy, Health and Human Services, Housing and Urban Development, Interior, Justice, Labor, State, Transportation, Treasury and Veterans Affairs.