"The four Al-Qaeda combatants were freed on Sunday night, after having served their sentence" of nine months in prison, a Malian security source told the AFP news agency.
On 30 January, Aqmi had extended a “final ultimatum” deadline to 20 February for the release of the prisoners, or they would kill Pierre Camatte, the French citizen whom they abducted in Mali in November.
On Sunday, Malian President Amadou Toumani Touré said he was hopeful that the six Europeans would be released, after a Malian negotiator had said that Camatte was alive and well.
"The French hostage is well, and so are the others," the negotiator told AFP, on condition of anonymity.
Aqmi is holding Camatte along with three Spaniards kidnapped in Mauritania in November and an Italian couple taken on 17 December, also in Mauritania.
On Sunday the Spanish newspaper El Mundo reported that Spain had reached a deal with the Malian authorities to pay a five million-dollar (3.7 million-euro) ransom for the release of the three Spaniards.
The group killed a British tourist in June last year after London did not meet their demands.