François Compaoré was arrested in Paris in October 2017 on an international arrest warrant. He is wanted on charges of "inciting" the death of an investigative journalist, Norbert Zongo, whose body was found, along with three others, in a burnt-out car in southern Burkina Faso December 1998.
Zongo was investigating the murder of a driver who worked for François Compaoré, and had written several hard-hitting articles about misrule in the Compaoré regime.
Blaise Compaoré was ousted in a popular revolt in October 2014 after trying to change the constitution to extend his 27-year rule. His brother was an economic adviser to the president, and had become one of the most disliked figures in the government.
Zongo's family has long accused Compaoré of being involved in the killings, which sparked protests in Burkina Faso.
François Compaoré’s lawyers argued against his extradition, saying the charges he faces in Burkina Faso do not exist in France, and warned he could face the death penalty.
French President Emmanuel Macron must still sign a decree authorising the extradition.
During a trip to Burkina Faso in November 2017, Macron said he would "do everything to facilitate" Compaoré's extradition.
Tuesday’s ruling, by France’s highest court, validated a lower court's decision. It can also be appealed in the Council of State, which rules on constitutional matters.