At a news conference, Obama also introduced retired Marine Gen.
James Jones as White House national security adviser, former Justice Department official Eric Holder as attorney general and Arizona Gov. Janet Napolitano as secretary of homeland security.
The announcements rounded out the top tier of the team that will advise the incoming chief executive on foreign and national security issues in an era marked by wars in Iraq and Afghanistan and terrorism around the globe.
"The time has come for a new beginning, a new dawn of American leadership to overcome the challenges of the 21st century," Obama said as his Cabinet picks stood behind him on a flag-draped stage.
"We will strengthen our capacity to defeat our enemies and support our friends. We will renew old alliances and forge new and enduring partnerships." Obama said his appointees "share my pragmatism about the use of power, and my sense of purpose about America's role as a leader in the world."
Gates' presence in Chicago made him a visible symbol of the transition in power from the Bush administration to one headed by Obama.
The president-elect, reprising a campaign vow, said he would give the military a new mission as soon as he takes office: "responsibly ending the war in Iraq through a successful transition to Iraqi control." He did not mention his oft-repeated pledge to withdraw most U.S. combat troops within 16 months.
He also appointed campaign foreign policy aide Susan Rice as his ambassador to the United Nations. Obama said he would make her a member of the Cabinet, an increase in stature from the Bush era.
Obama's announcements marked a shift in emphasis, after a spate of appointments last week for his economic team.
He now has selected half the members of his Cabinet, and is doing so at an unusually quick pace during his transition as he seeks to fulfill his goal of being able to "hit the ground running" when he takes the oath of office on Jan. 20.
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."
Clinton will give up her seat as a senator from New York to join the Obama Cabinet. Her appointment was preceded by lengthy negotiations involving her husband, the former president, whose international business connections posed potential conflicts of interests.
The former president also agreed to disclose the donors to the foundation that built his library, as well as contributors to his international foundation.
She said to Obama, in a brief turn at the lectern, "I am proud to join you ... and may God bless you and our great country."
Sen. Clinton had scarcely finished speaking when her husband issued a written statement. "She is the right person for the job of helping to restore America's image abroad, end the war in Iraq, advance peace and increase our security, by building a future for our children with more partners and fewer adversaries, one of shared responsibilities and opportunities," he said. Gates said he was "mindful that we are engaged in two wars and face other serious challenges at home and around the world."
"I must do my duty as they do theirs," he said of the men and women in uniform in Iraq, Afghanistan and elsewhere. "How could I do otherwise?" He said he was "honored to serve President-elect Obama."
Gates' appointment fulfilled a campaign promise by Obama, the naming of a Republican to his Cabinet.