Obama introduced Clinton first, saying of his former presidential rival: "She possesses an extraordinary intelligence and toughness, and a remarkable work ethic.
"She is an American of tremendous stature who will have my complete confidence, who knows many of the world's leaders, who will command respect in every capital, and who will clearly have the ability to advance our interests around the world."
Marwan Bishara, Al Jazeera's senior political analyst, said people hoping for fresh faces in Obama's team would be disappointed by the choice of established Washington-based figures but that others may argue that only those with significant experience could implement Obama's message of change.
All the appointments except that of national security adviser need to be approved by the US senate before they are confirmed.
Clinton, a New York senator and former first lady, clashed repeatedly with Obama on foreign affairs during the Democratic presidential primary campaign earlier this year.
|Clinton and Obama campaigned together after
Obama won the Democratic nomination [AFP]
Obama criticised Clinton for her vote to authorise the Iraq war.
And Clinton said Obama lacked the experience to be president condemning him for saying he would meet with leaders of nations such as Iran and Cuba without conditions.
However, on Monday, she stood alongside Obama and vowed to make the US a new force for positive change, saying that in her new role she would work with the world community to solve global crises.
"The American people have demanded not just a new direction at home, but a new effort to renew America's standing in the world as a force for positive change," Clinton told the Chicago news conference.
Clinton said she would "reach out to the world again" after eight years of the Bush administration and promised to give "this assignment, your administration and my country, my all".
Obama made the announcement just days after the Mumbai attacks added to the rising number of US national security concerns.
The president-elect, who is to take office on January 20, said he would give Gates a "new mission" to end the Iraq war and hand over control of the country to the Iraqis.
"I will be giving secretary Gates and our military a new mission as soon as I take office, responsibly ending the war in Iraq through a successful transition to Iraqi control," said Obama, pledging to focus on the fight against al-Qaeda and the Taliban in Afghanistan.
Gates had previously said he wanted to leave at the end of the Bush administration but agreed to stay on, although it is not clear for how long.
While Gates avoided direct criticism of Obama during the election campaign, he has advocated policies that have been at odds with Obama on issues such as Iraq.
Obama says he will withdraw US troops from Iraq within 16 months of taking office, but Gates has argued against setting timetables and a quick pullout, saying it could jeopardise security there.
Al Jazeera's Franc Contreras in Mexico City says Napolitano's appointment at the department of homeland security will be watched closely in Mexico as she will have responsibility for the border between the two countries.
"Napolitano has fought to curb illegal immigration, but has been sceptical that building a fence along the US-Mexico border will solve the problem. She once said: 'You build a 50-foot wall, somebody will find a 51-foot ladder.'"