Hollande now is set to become the only non-conservative leader in a major European country, and France's first left-wing leader in 17 years, the Globe and Mail reported.
The Socialist candidate defeated incumbent President Nicolas Sarkozy by 51.9 percent to 48.1 percent, vote count results showed after polls closed, the report said.
Thousands of Hollande supporters cheered outside the Bastille in Paris -- the traditional gathering-place for the left.
The last left wing leader of France was President Francois Mitterand, elected for the first of his two terms in 1981.
The newspaper said Hollande's election could mean a schism in how European countries respond to the euro debt-crisis.
Earlier, rain met French voters going to the polls in the runoff election. Polls in recent days favored Hollande, who beat Sarkozy by about 500,000 votes in the first round of voting on April 22.
Weather across much of France was rainy, which traditionally hurts turnout for leftist parties, Radio France Internationale reported.
Hollande's victory makes Sarkozy the 11th European leader voted out since the most recent recession, The Guardian newspaper reported from England.
France is in economic turmoil and the rating agency Standard & Poor's downgraded the country's triple-A credit rating because of high debt and record unemployment nearing 10 percent, the reports said.
Both Sarkozy and Hollande promised during their campaigns to balance the budget, which has not been done in more than 30 years, The Guardian said.