In Damascus, Maher al-Taher, the PFLP's spokesman, confirmed Habash's death. Habash had been living in Amman since 1992, he said.
The office of Mahmoud Abbas, the Palestinian president, has declared a three-day mourning period for Habash.
In Gaza, Ismail Haniya, the Hamas leader, said Habash "spent his life defending Palestine".
Later on Sunday, Khaled said Habash would be buried on Monday in Jordan.
"Funeral arrangements have been finalised and he will be buried in a suburban Amman cemetery following a funeral mass at the Greek Orthodox Latin rite church," she said.
Habash founded the PFLP, which promoted armed resistance, in December 1967 - six months after the war in which Israel seized east Jerusalem, the West Bank and the Gaza Strip.
The group was responsible for the hijackings of four Western airliners over the US, Europe, the Far East and the Gulf in 1970.
The aircraft were blown up in the Middle East after their passengers and crews had disembarked.
Born into a wealthy Christian Arab family, Habash became a refugee after the 1948 creation of Israel.
He graduated in 1951 from the American University of Beirut, going on to become a paediatrician.
He was a co-founder of Harakat Al Qawmeyon Al Arab, a pan-Arab nationalist movement founded in 1952 that has had a profound impact on Palestinian and Arab political thought.
Habash later espoused Marxism and emerged as an internationally recognised leader of the Palestinian liberation movement and the broader struggle for political and social justice.
For many Arabs, he was one of the few leaders who embodied the Palestinian cause.
His PFLP movement favoured armed struggle to establish a Palestinian state and opposed Arafat, breaking completely with him over the signing of the Oslo Peace Accords in 1993.
However, he wrote one of the most moving eulogies for Arafat.
Habash resigned as secretary-general of the PFLP in 2000, citing health reasons.