
Gates has said he wanted to leave at the end of Bush's last term and it is unclear how long he plans to serve in Obama's administration.
While he avoided direct criticism of Obama during the election campaign, Gates has argued against setting timetables for a US pullout from Iraq, saying it could jeopardize security gains made over the past year.
But Democrats and Republicans both praised Gates since he took over the Pentagon from Donald Rumsfeld in 2006 and he will provide continuity as the United States fights two wars.
Obama clashed with Clinton during a bitter campaign for the Democratic presidential nomination. Clinton famously ran an advertisement depicting a 3 a.m. crisis call at the White House to argue that Obama, a first-term Illinois senator, was not ready to be commander-in-chief.
Clinton also tended to talk tougher, once saying she would "obliterate" Iran if it attacked Israel. She criticized as "naive" Obama's call for direct presidential-level engagement with foes like Iran and North Korea.
Obama played down those differences on Monday, saying the two shared a vision for US foreign policy and wouldn't have joined forces if they didn't believe they could work together.
Clinton's husband, former President Bill Clinton, agreed to make public the names of more than 200,000 donors to his foundation as part of a deal with Obama to clear the way for his wife's nomination and avoid any appearance of conflict of interest with her duties as secretary of state.
Bill Clinton issued a statement praising his wife. "As an American, I am thankful," Clinton said. "As her husband, I am deeply proud."