Chirac, 83, was taken to hospital in Paris on December 9 after complaining he had felt "weak for a few days," his daughter Claude Chirac had said at the time, adding that there was no "cause for concern".
"He has returned home safely," a family member told AFP.
However journalists waiting outside Chirac's apartment building in the centre of Paris did not see him return, and a source told AFP the former president may now be residing in a new apartment nearby.
Chirac, who served two terms as head of state from 1995 to 2007 and is probably best remembered internationally for his opposition to the US military intervention in Iraq in 2003, was long known for the athletic physique and rude health that helped earn him the political sobriquet of "the bulldozer".
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However a small stroke while in office in 2005 weakened him, and he is now rarely seen in public and is reportedly confined to a wheelchair.
Chirac reportedly began to suffer from a degenerative neurological disorder during his last years in office, and that led prosecutors to spare him the humiliation of appearing in court in 2011 in a corruption trial.
In December 2013, Chirac underwent successful kidney surgery, and two months later he was briefly hospitalised for treatment of gout.
Chirac's wife Bernadette said in January 2014 that he suffers from periodic episodes of memory loss and expressed doubt he would ever speak in public again.
Chirac last attended a public ceremony in November 2014, where he was seen steadying himself upon one of his bodyguards.