Chirac also said on Wednesday that Sarkozy would leave his post as interior minister on March 26.
The announcement had been expected ever since Sarkozy said he would leave the centre-right government ahead of the first round of the election which will take place on April 22.
Chirac will step down after 12 years in office following the second round of the election in May, but there has been speculation over whether he would back Sarkozy's campaign.
Sarkozy had indicated he was expecting Chirac's support and said that failure to secure the president's endorsement could have damaged his credentials as the leading candidate of the right.
Relations between the two deteriorated after Sarkozy infuriated Chirac by backing his rival, Edouard Balladur, in 1995 presidential elections that Chirac went on to win.
Polls show Sarkozy currently leading the race to succeed Chirac in the April-May election, ahead of the Socialist Segolene Royal, 53, and the centrist Francois Bayrou, 55.
Far-right leader Jean-Marie Le Pen, 78, comes fourth, well ahead of the eight remaining candidates.
Chirac, who ruled out seeking a third term just 10 days ago, waited until the last possible moment to give his backing to Sarkozy, a one-time protege who is campaigning for a "clean break" with the policies of his government.
Royal's Socialist Party (PS) has accused Sarkozy of using his powers as interior minister - the number two position in the French government - to advance his campaign.
Sarkozy had dismissed the criticism, saying only that he would step down before the start of the official campaign on April 9.
He is expected to be succeeded at the interior ministry by overseas minister Francois Baroin, a protege of Chirac.