"I am happy because there are going to be many changes that will help the people and the working class," added construction worker Luis Astorga, 58.
Boric had campaigned on the promise of installing a "social welfare" state, increasing taxes and social spending in a country with one of the world's largest gaps between rich and poor.
Branded a "communist" by his detractors, he vowed in his first official address Sunday to "expand social rights" in Chile, but to do so with "fiscal responsibility."
"We will do it protecting our macro-economy, we will do it well... to improve pensions and healthcare," he said.
Kast congratulated Boric, who leads an alliance that includes Chile's Communist Party, "on his great triumph."
"From today on, he is the president-elect of Chile and he deserves all our respect and constructive cooperation. Chile always comes first."
Kast is an apologist for brutal dictator Augusto Pinochet and his neo-liberal economic model, credited with Chile's relative wealth but blamed for its deep-rooted social inequality.
He opposes same-sex marriage, contraception and abortion, and had initially pledged to close the ministry of women's affairs, a promise he later rowed back on.
According to a projection by Chile's Servel election body, turnout was more than 55 per cent -- a record since voting became voluntary in 2012.
Boric won by a margin of nearly a million ballots out of 8.3 million cast by 15 million eligible voters.
"Clearly more young people came out, it seems clear... that Boric managed to mobilise the segment that is more difficult to mobilize, which is the segment of young people," Claudia Heiss of the University of Chile told AFP.
"All (Kast's) anti-rights, anti-women, anti-gay speech, I think it helped mobilize that young segment," she added.
The new president will face the difficult task of healing a society reeling from a polarizing campaign replete with antagonistic attacks and fake news onslaughts.
For a country that has voted centrist since the democratic ousting of Pinochet 31 years ago, it was a stark choice between two polar opposite political outsiders.
Boric on Sunday reiterated his plans for "a more humane Chile, a more dignified Chile, a more egalitarian Chile."
Congratulations poured in from elsewhere in Latin America, from Brazil's ex-president Luiz Inacio Lula da Silva, Cuban leader Miguel Diaz-Canel and Argentina's Alberto Fernandez on the left, to right-wing presidents Ivan Duque of Colombia and Guillermo Lasso of Ecuador.
Boric and Kast had softened their policy proposals in a bid to appeal to Chileans left without an obvious candidate when they split the centrist vote in the first round, leaving only the two antipodes.
Both represent parties that have never been in government.
'President of all Chileans'
Chile is going through profound change after voting overwhelmingly last year in favor of drawing up a new constitution to replace the one enacted in the Pinochet years.
The 2020 referendum was in response to an anti-inequality social uprising in 2019 that left dozens dead.
The drafting process, in the hands of a largely left-leaning body elected in May, must yield a constitution for approval next year, on the new president's watch.
President Sebastian Pinera, who leaves office with a low approval rating, said Sunday the country was living in "an environment of excessive polarization, confrontation, disputes."
Pinera urged his successor, before the result was known, to never forget that "he will be the president of all Chileans, and not just those who support him."
Boric will be inaugurated in March next year.