Mr Fernández secured more than the 45% of the vote needed to win, beating conservative incumbent Mauricio Macri.
Raucous crowds gathered at Mr Fernández's election headquarters to celebrate the result.
The vote was held amid an economic crisis that has left a third of Argentina's population in poverty.
Mr Macri had trailed behind his challenger in pre-election polls and was trounced by the opposition in primary elections in August.
He conceded defeat on Sunday night. Congratulating his political rival, he said he had invited Mr Fernández to the presidential palace on Monday to discuss an orderly transition.
Mr Fernández later told supporters he would collaborate with the outgoing president "in every way we can", according to Reuters.
With more than 90% of ballots counted, Mr Fernández had 47.79% of the vote, compared to Mr Macri's 40.71%.
To win in the first round, a candidate needs at least 45% of the vote, or 40% and a 10-point lead over the second-place contestant.
Alberto Fernández will assume the presidency on 10 December.
At the Alberto Fernández campaign headquarters, people started gathering in celebration even before the result was out. Waving blue and white Argentine flags, many supporters also wore T-shirts with his face emblazoned on them.
But more ubiquitous was the image of Cristina Fernández de Kirchner, his vice-president and former leader. For many, she is a modern-day Eva Perón - a woman who has supported the poor with social programmes.
Her presence in this race clearly helped to propel Alberto Fernández to the top. So much so that many people, when asked who they were voting for, replied "Cristina" as if she was the one running for president rather than vice-president.
But she is a divisive figure, also accused of being corrupt and economically irresponsible.
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The chants from the crowds of "we will be back" came true. Alberto and Cristina - and Peronism - are back.
The challenge now will be to satisfy those who wanted a return to old politics, while convincing their critics they'll move the country forward.