A third diplomat, consul Boualem Sayes, had died in captivity "from a chronic illness", the ministry said.
It did not say whether Mourad Guessas and Kedour Miloudi had been released by their kidnappers or had been freed in a military operation.
The ministry did say however that Algeria had not paid a ransom to secure their freedom.
The two were released "after intense and tireless efforts" by authorities in "the utmost discretion", a statement said.
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It also confirmed for the first time the execution, reported in September 2012, of vice-consul Tahar Touati, describing his death as an "odious assassination".
Algeria's consul in Gao, in northeastern Mali, and six of his staff were taken hostage by MUJAO on April 5, 2012 while the Islamist militants were in control of the city.
Three jihadist groups, Al-Qaeda in the Islamic Maghreb (AQIM), Ansar Dine and MUJAO, in 2012 took control of much of the desert north of Mali, including the three main towns of Kidal, Gao and Timbuktu.