The estimates were carried by French media after all polling stations closed at 20:00 (18:00 GMT).
Hollande will be the first French socialist president of France since 1995.
He capitalized on France’s economic woes and President Sarkozy’s unpopularity. He has also promised to raise taxes on big corporations and people earning more than €1million a year, and lower the retirement age to 60.
Sarkozy, who has been in office since 2007, had promised to reduce France’s large budget deficit through budget cuts.
It is only the second time an incumbent president has failed to win re-election since the start of France’s Fifth Republic in 1958.
Hollande is expected to be inaugurated later this month. Analysts suggest this election result could have great implications for the entire eurozone.
Numbers show this election had a very high turn-out of voters, reaching a record high of over 80 per cent.