The announcement came after several days of uncertainty about the release of the pair, who were believed to have been held by al-Qaeda-affiliated militants.
Kidnapped Malian politician Soumaila Cisse, French aid worker Sophie Petronin and two Italian nationals have been freed after long periods in the hands of militants.
Their release follows a tense few days as reports the Malian authorities had freed scores of suspected militants over the weekend fuelled expectations of an imminent prisoner swap.
"The ex-hostages are on their way to Bamako," Mali's presidency said on Twitter.
The flight which is carrying them took off just before 7 pm local time (1900 GMT) from the northern town of Tessalit and was expected to arrive about 2 1/2 hours later, presidential spokesman Adam Thiam said.
French President Emmanuel Macron immediately voiced "immense relief" at the release of the worker and expressed France's continued support for Mali in its fight against an insurgency.
While relatives Cisse and Petronin had been notified of their release on Tuesday, news of the release of two Italian hostages came only in a Malian government statement once they were aboard the flight.
The Reverand Pierluigi Maccalli is a Roman Catholic missionary priest from the African Missionary Society (SMA) who was kidnapped in September 2018 from his Bomoanga parish in Niamey, Niger, according to the Avvenire newspaper of the Italian bishops conference.
There has been no information about Nicola Ciacco’s kidnapping except for the fact that he was seized in February 2018 in central Mali, according to Menastream, an independent risk and research consultancy firm specializing in the Sahel and North Africa. The two were believed to be held by same extremists though after a video was released of them together back in April.
Maccalli’s religious order, the Genoa, Italy-based African Missionary Society, said it had seen reports of Maccalli’s release but had no independent confirmation from the Italian foreign ministry.
A man who answered the phone at the order’s headquarters late Thursday said the order was nevertheless hopeful that Maccalli was returning.
Calls placed to the foreign ministry late on Thursday were not successful.
A popular politician
Cisse, a three-time presidential candidate, was travelling with his entourage in the north in March while campaigning for re-election as a member of parliament. Extremists ambushed his vehicle, killing his bodyguard, witnesses said. Cisse, 70, was injured by shattered glass, but little else is known about his conditions in captivity.
The only proof that Cisse was still alive was a handwritten letter delivered in August.
His re-emergence is likely to cast further uncertainty on the political scene in Mali.
He lost the 2013 and 2018 elections to Ibrahim Boubacar Keita, who was overthrown as president by the military junta in August after weeks of demonstrations organised by an opposition coalition.
While a transitional civilian government has been chosen, new elections are being organised with a 2022 deadline, providing a possible new avenue for Cisse.
Last known French citizen held hostage abroad
Petronin, 75, was believed to be the last known French citizen held hostage abroad, though abductions are sometimes kept under wraps while negotiations are ongoing.
In December 2016, militants seized Petronin from the city of Gao, where she was helping orphans as an aid worker. She appeared 18 months later in a video released on Telegram by the al-Qaeda-linked group known as JNIM.
Earlier Tuesday her nephew, Lionel Granouillac, told French radio RTL that Petronin’s son had taken a flight to Bamako on Tuesday morning.