Left-wing candidate Michelle Bachelet has been elected Chilean president for a second time by a wide margin.
With almost all the votes counted, Ms Bachelet had 62% against 38% for Evelyn Matthei, a former minister from the governing centre-right coalition.
Ms Bachelet first served from 2006 to 2010, but under Chile's constitution she could not stand for a second consecutive term.
She narrowly missed out on outright victory in the first round last month.
BBC Mundo's Ignacio de los Reyes said that hundreds of people applauded Ms Bachelet when she took to the stage outside the headquarters of her coalition in the centre of Santiago, some even cried with joy.
Many of them were women, members of the gay and lesbian community and environmentalists - some of the core groups that supported Ms Bachelet throughout her campaign.
In her victory speech, Ms Bachelet, 62, said she would carry out "deep reforms needed in Chile", but she assured voters she would do so "responsibly".
"Today in Chile we're in the majority and it's time we moved forward to fulfil the dream we all have, to again believe in ourselves, and to believe that there's strength in unity," she said.
"I am proud to be your president-elect today. I am proud of the country we've built but I am even more proud of the country we will build."
Ms Bachelet is now set to become the first leader in Chile to serve two terms since the military rule of Gen Augusto Pinochet from 1973 to 1990.
Upon hearing the news, her supporters took to the streets to celebrate, waving flags and sounding car horns in the capital, Santiago.
Her rival, Evelyn Matthei, 60, conceded defeat and congratulated Ms Bachelet in person.
Coming close to tears, Ms Matthei told her supporters that her "deepest and honest desire is that things go well for her [Michelle Bachelet]".
"No one who loves Chile can want anything else," Ms Matthei said.
Ms Bachelet thanked Ms Matthei for her good wishes and said that both shared a love for their homeland and a willingness to serve its people.
A paediatrician by training, Ms Bachelet won 47% of the vote in the first round on 17 November. Ms Matthei secured 25%.
Ms Bachelet leads an alliance of her Socialist Party, Christian Democrats and Communists and has campaigned on policies designed to reduce the gap between rich and poor.
Chile is one of the richest countries in Latin America, but millions have staged protests over the past few years to push for a wider distribution of wealth and better education.
Ms Bachelet wants to increase taxes to offer free university education and reform political and economic structures dating from the dictatorship of Gen Pinochet.
Her manifesto this time is much more radical than before, the BBC's Gideon Long in Santiago reports.
Ms Bachelet was constitutionally barred from serving a second successive term but was very popular when she left office.
Ms Matthei entered the race after two candidates of the centre-right alliance resigned earlier this year - one for alleged financial irregularities, the other one after struggling with depression.
She called for a continuation of the policies of outgoing President Sebastian Pinera, asserting that Chileans are "better off" now than when he came to power four years ago.
As children in the 1950s, the current rivals were neighbours and used to play together on the airbase where their fathers, both air force generals, worked.
Ms Matthei's father, Fernando, rose through the ranks to run a military school.
Michelle Bachelet's father, Alberto, had a job in the Socialist administration overthrown by Gen Pinochet in the 1973 coup.
He died in 1974 of a heart attack while in custody. An investigation concluded that the 51-year-old general had probably died of heart problems aggravated by torture at the military academy.
A judge ruled earlier this year that Gen Matthei had no knowledge of or involvement in the torture.