Large crowds have gathered to celebrate Michelle Bachelet's win

Her rival, conservative businessman Sebastian Pinera, has admitted defeat.

Giving a victory speech to cheering supporters, Ms Bachelet said: "Who would have said, 10, 15 years ago, that a woman would be elected president?"

The election is the fourth since Chile returned to democracy in 1990 after 17 years of military rule.

Outgoing President Ricardo Lagos hailed the election of Chile's first woman leader as a "historic triumph".

Pay homage

Mr Pinera, who had 46.5% of the vote with 97.5% counted, was also quick to congratulate Ms Bachelet.

Ms Bachelet thanked the thousands of enthusiastic supporters who gathered outside her campaign headquarters in the capital, Santiago.

She called on the whole country to work together to solve its problems and repeated her promise to bring more jobs and social justice to Chile.

The BBC's Daniel Schweimler in Santiago says thousands of people have been waving flags, blowing whistles and chanting slogans in the streets, with many more honking their horns as they drive round the city.

It took less than three hours after the polls closed for it to became clear the 54-year-old would be the next president and for the celebrations to begin.

Ms Bachelet has promised continuity, as head of the coalition which has led Chile for the past 16 years, but has also pledged change.

She has said she is keen to bridge the gap between rich and poor and to give a greater voice to women and indigenous people.

And, our correspondent says, more women are expected to be appointed to public office.

Unusual choice

The second round of voting was called after no candidate secured the 50% required for outright victory in the first round in December.

SOUTH AMERICAN WOMEN PRESIDENTS Michelle Bachelet - elected Chile's first woman leader, 2006 Janet Jagan - elected Guyana's leader in 1997 after the death of her husband, the previous president Lidia Gueiler Tejada - served as interim president of Bolivia following a coup, 1979-80 Isabel Martinez de Peron - sworn in as interim president of Argentina in 1974 when husband Juan Peron fell ill and died; kept power until 1976 Rosalia Arteaga - briefly acted as president of Ecuador in 1997

Ms Bachelet, who won 46% of the vote then, went into the run-off ballot leading the opinion polls.

The former defence minister will become the fourth consecutive president from the centre-left coalition known as the Concertacion, which has governed Chile since the end of military rule in 1990.

A doctor and a single mother, Ms Bachelet was seen as an unusual choice for the presidency in a country considered one of the most socially conservative in South America.

Mr Pinera - who polled 25% in December - was given the backing of third-placed candidate, Joaquin Lavin, who received 23% in that vote.

However, the billionaire businessman and former senator appears not to have picked up all the right-wing vote previously given to Mr Lavin.