By Daniel Schweimler
BBC News, Santiago
After months of campaigning and an inconclusive first round of voting, it came as something of a relief to most Chileans when it became obvious early on that a clear victor had emerged.
Bachelet celebrated with one of her daughters - and recalled her father
Less than three hours after polls closed, the first partial results were announced and Michelle Bachelet's supporters began gathering outside her campaign headquarters in central Santiago.
They blew whistles, proudly sported their "Bachelet presidente" T-shirts or hung from car windows waving huge flags.
Soon the streets of Santiago and other cities up and down Chile were thronged with happy supporters.
All the celebrations lacked was the centre of attention, Chile's new president, Michelle Bachelet.
She soon emerged, standing alone on the open-air stage outside her campaign headquarters in front of a huge Chilean flag.
"Who would have thought, just five years ago, that Chile would have a woman president?" she asked.
One issue notable by its absence during the campaign was the shadow still cast over Chile by the former military leader, Augusto Pinochet.
He has been watching proceedings from his home outside the capital while he is being investigated for financial irregularities.
Bachelet supporters were jubilant when the victory news came through
Some have accused the Chilean government of not dealing with those who committed human rights during the 17 years of military rule toughly enough.
But the most moving moment on an emotional night came when Ms Bachelet talked of her father, Alberto, who she said would have been the most proud of her victory.
The air force commander died after being tortured in the custody of General Pinochet's military government in the early 1970s.
Michelle herself and her mother were also detained but later released and fled to exile, first to Australia and then to Germany.
There, Michelle Bachelet continued her medical studies, later returning to Chile to practise her profession. She also joined the Socialist Party and worked her way through its ranks.
Under the government of President Ricardo Lagos, she served first as health and then defence minister. She obviously enjoys breaking into traditionally male areas.
In her victory speech, she went on to call for the whole population to work together to tackle the country's problems.
Pinera's defeat means the right must do some hard thinking
These include a growing gap between rich and poor, rising crime and unemployment and health and pension systems in need of reform.
Her defeated rival, the right-wing billionaire businessman, Sebastian Pinera promised to tackle those same issues, saying he would create one million new jobs and put 10,000 more police officers on the streets.
While both were promising to do much the same, Ms Bachelet seemed to instil more confidence among the electorate in her ability to carry out her tasks.
Mr Pinera was quick to congratulate Michelle Bachelet on her victory and wished her well for the future.
At the end of her term in office the right-wing will have been in opposition for 20 years and will now have to think how it will deal with the coming years if it is to ever set foot in the presidential palace.
Chile's economy is considered by most experts to be a success, certainly when compared to those of its neighbours.
A political analyst at New York University, a native Chilean, Patricio Navia, said the new president would not have to deal with any immediate emergencies but would have a number of pressing problems to deal with.
Among those problems on Michelle Bachelet's list of things to do when she takes up her new job in March will be the widening gap between rich and poor, rising unemployment and growing crime.
Chile has the money to reform and tackle its problems, mostly as the result of high world copper prices, one of the country's major exports.
President Michelle Bachelet also has a sound and experienced party machine behind her, a strong mandate from the Chilean electorate to govern and a fresh approach to a job that has traditionally been for men only.