The two men are the only living Democrats who have occupied the White House. Clinton was accompanied by his wife, Secretary of State Hillary Rodham Clinton, who is departing as Obama's second term gets under way.
Former first lady Rosalynn Carter accompanied her husband for the ceremonies at the Capitol's West front.
Neither former President George W. Bush nor his father, former President George H.W. Bush, were expected to attend. Both are Republicans.
The elder Bush was recently released from the hospital, where he was treated for bronchitis and other issues.
(Copyright 2013 by The Associated Press. All Rights Reserved.)