A former student activist who was once tortured and exiled by the country's armed forces, Bachelet previously served as a health and defence minister.
Among those attending Bachelet's inauguration on Saturday was Condoleezza Rice, the US secretary of state.
Helen Clark, the prime minister of New Zealand, and Fatemeh Javadi, Iran's vice-president, also attended the ceremony in the port city of Valparaiso.
Ahead of formally taking office, Bachelet had already appointed a cabinet with an equal number of men and women, and vowed to do the same in 300 decision-making positions in the government.
She has promised to promote legislation that would force political parties to include a certain percentage of female candidates.
Bachelet, a separated mother of three, is the first elected female Latin American leader who did not rise to power with the help of a powerful husband.
Bachelet's election is being seen as evidence of Chile's profound political transformation since the end of the dictatorship by General Augusto Pinochet in 1990.
Iran's vice-president(L) is among
those attending the inauguration
She is the daughter of an air force general who was tortured and died in prison for opposing the 1973 military coup led by Pinochet.
And she, too, was briefly imprisoned and tortured along with her mother before being forced into exile.
Bachelet was elected on 15 January for a four-year term in a runoff vote to succeed fellow socialist Ricardo Lagos, who is leaving power with an approval rating of more than 70%.
In a nationally broadcast farewell address to the nation, Lagos said, "I will be proud to hand the presidency to a woman for the first time in Chile's history".
Lagos called Bachelet "a symbol of a country that has advanced towards new challenges, a society that has changed deeply for the better towards liberty, pluralism, equality".
"[A] symbol of a country that has advanced towards new challenges, a society that has changed deeply for the better towards liberty, pluralism, equality"
Outgoing president on his successor
Under Bachelet's leadership, "Chile will consolidate its achievements and will reach new victories", Lagos said.
Bachelet is seen politically as farther to the left than Lagos, although she is expected to retain Chile's successful economic policies that stress open markets and have led the South American nation to sign free trade accord with the United States, the European Union, Canada, Mexico and South Korea, among others.
Few major changes are expected in foreign policy either. In a consular document issued on Friday with information about Chile, mainly for tourists and investors, the US State Department has said relations with Chile are at its best level ever.
But Bachelet has made it clear that she will give priority to relations with Latin American countries, where several leftist leaders have been elected.
Bachelet has sought to dispel the idea that she should be treated differently than male politicians, dismissing questions abruptly about how she dresses or her love life.
But occasionally, she turns to humour. When a well-known psychologist publicly suggested that she should lose weight, Bachelet replied: "A friend told me that if I do that, voters would lose the motherly image they are looking for in me."