About 30 foreign leaders and several prominent women, including Secretary of State Condoleezza Rice, attended.
Rice offered congratulations to Bachelet, a socialist taking office more than three decades after a US-linked coup that ousted the country's elected leftist leader.
The inauguration of Bachelet, a former health and defense minister, represented the triumph of democracy over a troubled history, Rice said.
The two met for about 30 minutes in this port city about 75 miles northwest of Santiago, but made no public comments afterward. At the swearing-in ceremony, Rice sat next to Mexico's foreign relations minister, Luis Derbez.
Bachelet's inauguration marks a deep cultural change in this male-dominated, conservative society, where divorce was legalized less than two years ago, abortion remains illegal, and women often earn up to 40 percent less than men doing the same work.
Already, she's challenged the traditional power structure by appointing what she calls a ''parity government" -- with equal numbers of men and women at more than 250 key jobs. She made the appointments without the traditional, lengthy negotiations with the political parties.
In addition, Bachelet has also vowed to promote legislation that would force political parties to include a certain percentage of female candidates.
Bachelet was elected to a four-year term in a Jan. 15 runoff vote to replace Lagos, a fellow Socialist. The United States counted Chile under Lagos as an example of a leftist government with which Washington enjoyed strong economic and political ties.
At an International Women's Day celebration, Lagos called Bachelet's election ''proof that we have expanded the limits of what is possible in Chile nowadays."
A separated mother of three, Bachelet is the first elected Latin American leader who didn't rise to power with the help of a powerful husband. She says her victory reflects profound changes in Chilean society.
Bachelet is the daughter of an Air Force general who was tortured and died in prison for opposing the 1973 military coup led by General Augusto Pinochet. She, too, was briefly imprisoned and tortured before being forced into exile.
She is expected to maintain Lagos's free-market economic policies that have made Chile's economy one of the healthiest in Latin America. The country had a $5 billion surplus in 2005.
