Describing Bana as the girl "who announced the Aleppo massacre to the world on social media", Cavusoglu told state-run Anadolu that she and her family would be brought to Turkey.
On Sunday, Bana's mother sent a Tweet urging Turkish President Recep Tayyip Erdogan and Cavusoglu to help evacuate them. Turkey helped broker the ceasefire deal that made the evacuations possible.
Ahmad Tarakji, president of the the Syrian American Medical Society (SAMS), tweeted on Monday that Bana had been safely evacuated to the Aleppo countryside.
Zaher Sahloul, a SAMS relief coordinator, tweeted that Bana was "safe with her family," adding that she survived "siege, bombing & apathy."
Bana has two brothers Mohammed, 5, and Noor, 3, along with her mother and father. The young pig-tailed, gap-toothed girl kept a harrowing log of the conflict on Twitter with the help of her mother, Fatemah Alabed.
Following the evacuation, mother Fatemah spoke of her sadness at leaving Aleppo
, saying she had "left her soul" in Eastern Aleppo.
"When we got out we had a lot of suffering because we stayed almost 24 hours in bus without water and food or anything.. like a prisoner," she told to pro-opposition media organization Qasioun News.
"But finally we arrived here and we thank God and all our friends who are supporting us."
At moments, Bana and her family posted their experiences as they were in imminent threat of being hit in airstrikes, carried out by the Syrian regime and its ally, Russia.
Three months ago, Alabed, an English teacher with a spotty Internet connection, decided she wanted the world to hear her children's voices and see their faces, hoping that maybe she could galvanize global support for those in Aleppo.
Bana has since then become embodiment of the human toll this grinding conflict has had on the children of Syria.
Bana's family had been in hiding since their home was reduced to rubble on November 27, their location unknown.
Evacuations of civilians and rebels from Syria's eastern Aleppo resumed late Sunday after several hours of delay.
The exodus of thousands of people from besieged areas began last week, but was suspended several times as ceasefires were violated and warring parties negotiated new terms to the deal.
They resumed on Sunday under a new complex people-swap deal after being delayed for more than 12 hours when a number of buses deployed for the evacuations were set on fire.