Air traffic controllers lost contact with the plane early on Thursday after pilots reported severe storms.
The passengers included 51 French citizens.
The McDonnell Douglas MD-83 – Flight AH 5017 – had been chartered from Spanish airline Swiftair.
Malian state television confirmed that the wreckage was found in the village of Boulikessi by a helicopter from Burkina Faso, the Associated Press news agency reports.
Gilbert Diendere, a Burkina Faso army general, said Mali had agreed to their cross-border search which was launched after a resident in Gossi described seeing a plane go down to the south-west of the town.
“They found human remains and the wreckage of the plane totally burnt and scattered,” he told AP.
French fighter jets and UN helicopters had been hunting for the wreck in the more remote desert region of northern Mali between Gao and Tessalit.
Contact with Flight AH 5017 was lost about 50 minutes after take-off from Ouagadougou on Thursday morning, Air Algerie said.
The pilot had contacted Niger’s control tower in Niamey at around 01:30 GMT to change course because of a sandstorm, officials say.
Burkina Faso authorities said the passenger list comprised 27 people from Burkina Faso, 51 French, eight Lebanese, six Algerians, two from Luxembourg, five Canadians, four Germans, one Cameroonian, one Belgian, one Egyptian, one Ukrainian, one Swiss, one Nigerian and one Malian.
The six crew members are Spanish, according to the Spanish pilots’ union.
The crash adds yet new worries to air transport passengers following two other aircraft accidents in under a week, About a week ago Malaysian airline MH17 was shot down by Ukranian rebels while another aircraft crashed in the Philines with about 50 people on board.
Another huge aircraft MH 370 belonging to Malaysian airlines disappeared in the Pacific Ocean in March this year with hundreds of people on board.