Mr Lagos, a long-time opponent of former military dictator General Augusto Pinochet, is the first socialist to be elected head of state since Salvador Allende in 1970.
His right-wing rival, Joaquin Lavin, who once worked in General Pinochet's government, congratulated and embraced Mr Lagos on his victory.
In a speech at a rally near the presidential palace, Mr Lagos told his supporters he would be the president of all Chileans.
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But he made it clear the priority for his government would be bringing Chile out of its first economic recession in more than a decade.
Close result
Thousands of Chileans took to the streets of the capital Santiago to celebrate Mr Lagos' win.
With nearly all votes counted, Mr Lagos had 51.3% to Mr Lavin's 48.6%, making it one of the closest races in Chile's history.
Mr Lavin had forced the election to a second round after the first round in December produced no clear winner - with only 0.5% separating the two men.
Mr Lagos is due to be inaugurated on 11 March for a six-year term, succeeding Eduardo Frei, a Christian Democrat who was constitutionally barred from re-election.
The 61-year-old economist will be the third president of the centre-left coalition, which has governed Chile since the return to democracy 10 years ago.
Pinochet factor
The run-off vote came just five days after the UK said it might release General Pinochet on health grounds.
Mr Pinochet was detained last October on a warrant from a Spanish judge who wants him to stand trial for human rights abuses.
Mr Lagos, who was imprisoned briefly by General Pinochet in the mid-1980s, has supported efforts to get him sent home, saying he should be tried in Chile.
However neither Mr Lagos nor the pro-Pinochet Mr Lavin made much of the issue in their campaigns - both focusing instead on day-to-day matters such as health, education and unemployment.
Mr Lagos limited himself to a brief attack on Mr Lavin, saying it was a good thing Mr Lavin did not wish to discuss the past, because the past so clearly condemned him.
Although Mr Lagos backed the former socialist president, Salvador Allende, who was toppled by General Pinochet in a 1973 coup, he has dismissed claims that his election would signal a return to Allende-style Marxism.