The papal plane, Shepherd 1, touched down at Andrews Air Force Base in Maryland to cheers from a crowd of invited guests gathered for the event.
After he stepped off the plane, Benedict did not kiss the ground, as his predecessor, Pope John Paul II, often did during visits.
The pontiff was greeted by President Bush, first lady Laura Bush and their daughter Jenna, each of whom shook his hand.
It was believed to be the first time an American president has greeted a world dignitary on arrival at Andrews.
"It had the look and feel of a monumental and historic event," CNN's Brian Todd reported.
This is the first U.S. papal visit since the attacks of September 11 and Benedict's first visit to the United States.
There will be a welcoming ceremony for the pope on the South Lawn of the White House on Wednesday. Benedict is to speak before meeting with U.S. cardinals and bishops.
One of the stated goals of the pope's visit is to energize the U.S. Catholic community: the largest in the world, with an estimated 70 million members.
Three years after succeeding Pope John Paul II, Benedict is likely to address the sex scandal within the Catholic Church, the church's relationship with other faiths, the U.S.-led war in Iraq and the upcoming U.S. presidential election, said John Allen, a CNN Vatican analyst.
The fallout from the sex scandal has had a serious impact on the U.S. Catholic Church in terms of its finances, its moral authority and the demoralization of Catholics.
During the flight from Rome to Washington, the pope told reporters aboard that he was ashamed of the problem.
Meanwhile, security preparations were under way in the air, on land and in the water.
Twenty-seven state, local and federal agencies will protect the pope as he meets with religious leaders, celebrates Mass at a baseball stadium and makes his way around the capital in his distinctive "popemobile."
There are no specific threats against Benedict, according to the FBI, but a March audio message from Osama Bin Laden mentioned the pontiff.
The centerpiece of the Washington leg of the U.S. visit will be Thursday's Mass at Nationals Park, a new baseball stadium where 46,000 people will gather to watch the pope. Everyone will go through metal detectors on their way in, and nearby roads and bridges will be closed. Temporary flight restrictions will be in place over the stadium.
A 1½-mile section of the adjacent Anacostia River will be closed during the Mass. The Coast Guard will patrol the river in boats with machine guns mounted on their bows.
"I am worried about a terrorist attack," said Lt. Lynda LeCrone of the Coast Guard. "We are here to detect, deter and defend against waterborne attack on this highly publicized event. ... We can use force."
The pope will be making his way around parts of Washington in the popemobile, a Mercedes Benz modified with bulletproof glass surrounding a seating area from which the pope can wave to bystanders along his route.
The vehicle, one of three popemobiles in the Vatican motor pool, arrived in the United States last week. It will be driven by a Secret Service agent. The agents have been training with the vehicle.
"We try best-case scenarios and also try worst-case scenarios so our staff will know how to react," said Secret Service Special Agent Renee Triplett, who oversees Secret Service training.
Benedict will travel to New York on Friday and address the U.N. General Assembly, linking the visit to the 60th anniversary of the Universal Declaration of Human Rights. He'll celebrate Mass Sunday morning at Yankee Stadium.
Still a mystery
Despite three years as the head of the Catholic Church, the pope remains a bit of a mystery to many American Catholics.
"I think most American Catholics may not know a whole lot about him," Allen said. "He's not the sexy media icon that John Paul II was, but what they've seen, by and large, they've liked."
Of American Catholics polled by the Pew Research Center, 74 percent give Pope Benedict a favorable rating. But the survey points out that he's not as highly regarded as his predecessor
For one, their personalities are different. John Paul was known for his charisma. Benedict is known as an intellectual and introvert.
"He doesn't quite get the same energy from crowds that John Paul II got," said Cardinal Francis George, president of the U.S. Conference of Catholic Bishops. "John Paul II was extroverted and got energy talking to people, and the present Holy Father loses energy. He has to rest between all these encounters."
The energy factor is partly due to age. Benedict turns 81 this week. When John Paul became pope, he was only 58 and was able to keep a much more rigorous schedule traveling around the globe.