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With results announced at more than 96% of polling stations, the first lady - wife of President Néstor Kirchner - had about 45% of the vote, compared with 23% for her chief rival, Elisa Carrió, and 17% for the former economy minister Roberto Lavagna.
Mrs Kirchner now has an unassailable lead and is due to be officially confirmed as Argentina's first elected female head of state.
"We have won amply," she said. "But this, far from putting us in a position of privilege, puts us instead in a position of greater responsibilities and obligations."
She also claimed some credit for the economic progress made during her husband's presidency after the economic crisis of 2001, when the economy grew by 50% and unemployment halved.
"We have repositioned the country, fought poverty and unemployment, all these tragedies that have hit Argentines."
Ms Carrió has already conceded defeat. In a broadcast speech she said: "We congratulate and recognise her victory."
However, her spokesman said seven parties had made an official complaint alleging missing or stolen ballots. One representative of the ruling party was arrested on suspicion of trying to vote twice.
Mrs Kirchner, a former lawyer, is expected to maintain leftwing populist economic policies, such as price controls, and to inject glamour and energy into Argentine diplomacy. Her husband, dour and proudly provincial, loathed foreign trips, but was feted at home for overseeing the economic recovery. One challenge will be to maintain good relations with President Hugo Chávez of Venezuela, who has poured billions of dollars into Argentina's economy, while improving ties with Washington.
Mr Cháavez telephoned Mrs Kirchner last night to congratulate her. "This is a triumph of the women of Latin America, because women are going to save the world," he said, according to Venezuela's state-run Bolivarian News Agency.
Kirchner supporters did not wait for the official results. The campaign headquarters on the 17th floor of the Intercontinental hotel in Buenos Aires soon turned into a party. Drummers bussed in from Bajo Flores, a poor district of the city, gathered on the street outside for what promised to be a night-long fiesta.
Yesterday's victory sealed a remarkable pact between the first couple. Mr Kirchner would almost certainly have won a second term after delivering rapid growth and populist policies, which most Argentines want to continue.
Instead, he stepped down in favour of his wife and mobilised the Peronist machine - and state resources - behind her candidacy. There is speculation that he may run again after her term, perpetuating a Kirchner dynasty.
"The president chose her because she's the best candidate," said Felipe Martinez, 39, one of the revellers outside the Kirchner headquarters. "Today we've seen that the people have put their confidence in her. We expect her to continue in the same path."
Mr Martinez was dressed as a penguin in honour of the first couple's Patagonian power base. Mr Kirchner's nickname is the Penguin. The couple's success has been dubbed March of the Penguins.
The first lady, who is a 54-year-old mother of two and veteran politician in her own right, has been compared with Eva Perón and Hillary Clinton.
Unlike the US Democrats' frontrunner, however, she has not had to campaign hard, debate with rivals or spell out policies on inflation, crime and a looming energy crisis - serious problems that could quickly sour her presidency.
With her victory seemingly inevitable in a crowded field of 13 rivals, Mrs Kirchner's campaign had the aura of a coronation. She shunned debates with rivals, largely ignored the media and held few rallies.
"We don't know what plans she has. She hasn't said anything," Mr Lavagna said earlier.
The country's 27.1 million registered voters were obliged to vote, ensuring a good turnout, but the campaign was marred by widespread apathy, which gave no sense that the first election of a female president was historic.
Mrs Kirchner will be the most powerful woman in Latin America, as President Michelle Bachelet of Chile, the region's only other female head of state, heads a much smaller economy.
After casting her ballot in the morning Mrs Kirchner told reporters that she savoured voting because of the 1976-1983 dictatorship. "I'm part of a generation that grew up in a country in which nobody could say anything. So we value this in a very special way," she said.
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