A court hearing on Verhoeven's case was held in New Delhi on Wednesday and the Chilean government had complained.
The Indian foreign ministry said Verhoeven, who had been held in the country since February 2015, was released at France's request on health grounds.
Verhoeven's Indian lawyer confirmed that proceedings against her had been halted.
"The government withdrew the extradition proceedings against her and the matter was closed," Ramni Taneja, Verhoeven's lawyer, told AFP.
A source close to the case said the Frenchwoman, 57, had been put on a plane to Paris.
A court hearing on Verhoeven's case was held in New Delhi on Wednesday and the Chilean government had complained at India's failure to hand her over.
The Indian foreign ministry said: "Having considered the matter in its entirety, including the French request, the deteriorating mental and physical health of Ms. Marie Emmanuelle Verhoeven and the commitment of the French Government in the matter, the government decided ... to withdraw its inquiry order."
It added the government "discharged Ms. Marie Emmanuelle Verhoeven on medical and humanitarian grounds".
The ministry said that the French government also committed to "subsequent bilateral examination of the matter with the country directly concerned" while requesting for her return to France on health grounds.
Chile has been seeking the extradition of Verhoeven over her alleged role in a conspiracy to kill Senator Jamie Guzman Errazuriz on April 1, 1991.
The senator was close to Chile's late dictator Augusto Pinochet. The killing was blamed on an extreme left wing group and Chilean investigators said Verhoeven was known as "Commander Ana" in the group.
It was the second time that Verhoeven has avoided extradition to Chile over the case. She was detained in Hamburg, Germany in January 2014, but German authorities rejected Chile's request.
Indian police arrested Verhoeven following an Interpol alert as she entered the country overland from Nepal.
She subsequently spent almost 16 months in a New Delhi high security prison before she was released on bail.
Verhoeven told authorities that she was visiting India on a Buddhist pilgrimage and her lawyers challenged a treaty between India and Chile allowing for her extradition.
Lawyers argued that the treaty, dating back to the 1800s, was not constitutional because it was not ratified after independence and the Partition of India in 1947.
India's Supreme Court last year ruled in favour of the government which argued that the treaty was still valid and so Verhoeven had to face the extradition proceedings.